CBSE Class 6 Mathematics Playing With Numbers Worksheet Set A

Find the LCM of the numbers given below :

Question. 42,63
Answer :

42 = 2 × 3 × 7
63 = 3 × 3× 7 =
3² × 7
∴ LCM of 42 and 63
= 2 × 32 × 7
= 2 × 9 × 7
= 18 × 7
= 126

Question. 60,75
Answer :

60 = 2 c 2 × 3 × 5
= 2² × 3 × 5 75
= 3 × 5 × 5
= 3 × 52
∴ LCM of 60 and 75 = 2² × 3 × 5²
= 4 × 3 × 25
= 12 × 25
= 300

Question. 12,80,20
Answer :

12 = 2 × 2 × 3 = 2² × 3
18 = 2 × 3 × 3 = 2 × 3²
20 = 2 × 2 × 5 = 2² × 5
∴ LCM of 12, 18, and 20 = 2² × 3² × 5
= 4 × 9 × 5
= 180

Question. 36,60,72
Answer :

36 = 2 × 2 × 3 × 3 = 2² × 3²
60 = 2 × 2 × 3 × 5 = 2² × 3 × 5
72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
∴ LCM of 36, 60 and 72 = 2³ × 3² × 5
= 8 × 9 × 5
= 72 × 5
= 360

Question. 36 40,126
Answer :

36 = 2 × 2 × 3 × 3 = 2² × 3² 4
0 = 2 × 2 × 2 × 5 = 2³ × 5
126 = 2 × 3² × 7
∴ LCM of 36, 40 and 126 = 2³ × 3² × 5 × 7
= 8 × 9 × 5 × 7
= 72 × 35
= 2520

Question. 144,180,384
Answer :

∴ LCM of given numbers = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 8
= 2⁴ × 3² × 5 × 8
= 16 × 9 × 5 × 8
= 16 × 45 × 8
= 5760

Question. 48,64,72,96,108
Answer :

∴ LCM of given numbers = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 2 × 3
= 2⁶ × 3³
= 64 × 27
= 1728

Find the HCF and LCM of

Question. 117,221
Answer : To find the HCF of 117 and 221

∴ HCF of 117and 221 = 13
Since, LCM = product of numbers/HCF
= 117 × 221/13
= 9 × 221 = 1989 ∴ LCM
= 1989 and HCF = 13

Question. 234,572
Answer : To find the HCF of 234 and 572

∴ HCF of 234 and 572 = 26
Since, LCM = Product of numbers/ HCF
= 234 × 572/ 26
= 9 × 572 = 5148
∴ LCM = 5148 and HCF = 26

Question. 693,1078
Answer : To find the HCF of 693 and 1078

∴ HCF of 693 and 1078 = 77
Since, LCM = Product of numbers/ HCF
= 693 × 1078 / 77
= 9 × 1078
= 9702
∴ LCM = 9702 and HCF = 77

Question. 145,232
Answer : To find the HCF of 693 and 1078

∴ HCF of 145 and 232 = 29
Since, LCM = product of numbers / HCF
= 145 × 232 / 29
= 5 × 232
= 1160
∴ LCM = 1160 and HCF = 29

Question. 861,1353
Answer : To find HCF of 861 and 1353

∴ HCF of 861 and 1353 = 123
Since, LCM = product of numbers /HCF
= 861 × 1353 / 123
= 7 × 1353
= 9471
∴ LCM = 9471 and HCF = 123

Find the product using suitable laws:

1. 968 X 73 + 968 X 27

2. 8937 X 648 + 8937 X 122 + 8937 X 230

3. 23756 X 999

4. 16825 X 16825 – 16825 X 6825

5. 4 X 927 X 50

6. 625 X 20 X 8 X 50

Q.1 Write all factors of each of the following numbers.
(i) 24
(ii) 300
(iii) 225

Q.2 Write first five multiples of each of the following numbers
(i) 12
(ii) 36
(iii) 18

Q.3 Write all prime numbers between
(i) 20 and 40
(ii) 80 and 100

Q.4 Express each of the following numbers as the sum of two odd primes
(i) 45
(ii) 39
(iii) 64

Q.5 Express each of the following numbers as the sum of three odd primes
(i) 63
(ii) 53
(iii) 15

Q.6 Express each of the following as the sum of twin primes
(i) 36
(ii) 84

Q.7 Find prime factorization of each of the following numbers
(i) 1331
(ii) 1024
(iii) 148

Q.8 Find the product using distributive property of multiplication over addition or subtraction.
a) 289 x 1001
b) 1572 x88 + 1572 x 11 +1572
c) 4765 x 998
d) 1987 x 95 + 1987 x 5

Q.9 Find the product by suitable rearrangement
a) 4 x 345 x 16 x 25 x 625
b) 698 x 5 x 20
c) 625 x 279 x 32 x 50
d) 4 x 80 x 125 x 75

Q.10 Q9 Find the sum using associative property
a) 545 + (346 + 113)
b) (67 + 78)+ 42

Q.11 Find the HCF of the following numbers using prime factorization method
(i) 72, 144 and 252
(ii) 60 and 72
(iii) 225, 1125 and 5625

Q.12 Determine the HCF of the following numbers by division method
(i) 675, 900
(ii) 615, 1599
(iii) 180, 252, 324

Q.13 Determine the LCM of the numbers given below
(i) 48, 72 and 84
(ii) 28, 36, 45 and 60
(iii) 12, 24, 36 and 54

Q.14 The LCM and HCF of two numbers are 6055 and 173 respectively. If one of the numbers is 267, find the other.

Q.15 The LCM of two numbers is 525 and 945 is 4725. Find their HCF.

Q16 Express
a) 3 months as a fraction of 1 year b) 40g as a fraction of 1 kg
c) 35p as fraction of 1 rupee
d) 2 scores as a fraction of 1 century

Q17 Find the equivalent fraction of (i) 45 (ii) 37

Q18 Represent the following fractions on number line (i) 1/3 (ii) 45 (iii) 57

Q19 Find equivalent fractions of 40/48 with:
a) Numerator = 5
b) Denominator = 12

Q20 Anu plays for ⅘ of an hour while Richa plays for ⅜ of an hour. Who plays for more time?

1M

1.The twin prime numbers out of the following are:
(A) 2,4
(B) 3,5
(C) 7,11
(D) 13,17

2.In the following which pair of numbers is co-prime?
(A) (2,4)
(B) (2,3)
(C) (3,9)
(D) (4,16)

3.Which number is a multiple of 11?
(A) 122
(B) 132
(C) 110
(D) (2) and (3) both

4.The least number which when divided by 9, 12, 16, 30 leaves a remainder of 3 in each case is
(A) 720
(B) 723
(C) 823
(D) 750

5.Which of the following number is divisible by 11 ?
(A) 3,116,365
(B) 901,351
(C) 8,790,322
(D) None of these

6.The prime factors of 24 are
(A) 2 × 3 × 4
(B) 2 × 2 × 2 × 3
(C) 6 × 4
(D) 8 × 3

7.What least value should be given to * so that the number 653*47 is divisible by 11 ?
(A) 9
(B) 6
(C) 2
(D) 1

8.The sum of the prime numbers between 90 and 100 is
(A) 188
(B) 281
(C) 376
(D) 97

9.A prime number
(A) has exactly one factor
(B) has exactly two factors
(C) is not divisible by 2
(D) is an odd number

10.Least prime number is
(A) 1
(B) 0
(C) 2
(D) 3

11.A prime number is
(A) an even number
(B) an odd number
(C) a composite number
(D) None of these

12.The smallest number of 4- digits exactly divisible by 12,15, 20 and 35 is
(A) 1000
(B) 1160
(C) 1260
(D) None of these

13.Successor of every even number is
(A) Even
(B) Prime
(C) Odd

(D) None

14.Prime factors of 140 are
(A) 2 × 2 × 7
(B) 2 × 2 × 5
(C) 2 × 2 × 5 × 7
(D) 2 × 2 × 5 × 7 ×3

15.HCF of two co- prime number is
(A) 1
(B) 0
(C) 2
(D) None of these

16.HCF of 36 and 144 is
(A) 36
(B) 144
(C) 4 (D) 2

17.An example for twin primes is
(A) 5, 11
(B) 3, 5
(C) 11, 17
(D) 3, 7

18.LCM of 36 and 72 is
(A) 36
(B) 72
(C) 108
(D) 2

19.The number which is neither prime nor composite is
(A) 0
(B) 1
(C) 2
(D) 5

20.The numbers which have more than two factors are called
(A) Even
(B) Prime
(C) Composite
(D) None of these

21.The numbers which are not multiple of 2 are called
(A) Even
(B) Odd
(C) Prime
(D) Composite

22.The two numbers which have only 1 as their common factor are called
(A) Co-primes
(B) Twin prime
(C) Composite
(D) None of these

23.How many prime numbers are there between 10 to 20 ?
(A) 5
(B) 7
(C) 4
(D) 3

24.Which of the following numbers is not a multiple of 8 ?
(A) 64
(B) 4
(C) 16
(D) 80

25.Which number is not a factor of 18 ?
(A) 5
(B) 3
(C) 2
(D) 6

26.The Number which is a factor of every number is
(A) 0
(B) 1
(C) itself
(D) both 1 & 0

27.The smallest 5-digits number, which is exactly divisible by 9,15,18, is:
(A) 999
(B) 9990
(C) 99989
(D) 9995

28.Predecessor of every even number is:
(A) Prime number
(B) Odd number
(C) Both
(D) None

29.Greatest 4-digit number which is divisible by 4,6,12 is…….
(A) 9997
(B) 9996
(C) 9998
(D) 9995

30.1 is a/an………
(A) Integer
(B) Irrational number
(C) Natural number
(D) None

31.The sum of all prime numbers between 10 to 25 is..
(A) 84
(B) 86
(C) 85
(D) 83

32.The smallest prime number is ____

33.The number 1 is neither ______ nor _______

34.The H.C.F of two prime numbers is _____

35.Are (11, 13) twin- prime Numbers?

36.34 can be expressed as the sum of two prime no's _____and _____

37.are (49, 51) Co-prime Numbers

38.Find the least common multiple of 6 and 8

39.The Number which is a factor of every number

40.The numbers which have more than two factors are called

41.The numbers which are not multiple of 2 are called ___________

42.The two numbers which have only 1 as their common factor are called _________

43.Which is the greatest prime numberout of the following?
(A) 2
(B) 3
(C) 91
(D) 97

44.Which of the following number is divisible by 6?
(A) 12930
(B) 12935
(C) 12933
(D) 12934

45.Which of the following number is divisible by 9?
(A) 2952
(B) 2953
(C) 2954
(D) 2950

46.The definition of composite number.
(A) A number, which has more than two factors, is called a composite number.
(B) A number, which has exactly two factors, is called a composite number.
(C) Both (a) and (b)
(D) None

47.First three odd numbers are ........................ and first three even number are………………….
(A) 1, 3, 5 and 2, 4, 6
(B) 0, 1, 2 and 0, 2, 4
(C) 2, 3, 5 and 4, 6, 7
(D) 2, 4, 6 and 1, 3, 5

48.The H.C.F of 9 and 27:
(A) 9
(B) 3
(C) 2
(D) 27

49.Every number is a multiple of ……..
(A) 0
(B) 1
(C) -1
(D) none

50.The prime numbers between 0 to 20 are:
(A) 2,3,5,7,11,13,17,18
(B) 2,3,5,7,11,13,17,20
(C) 2,3,4,5,6,7,8,9,10,11
(D) 2,3,5,7,11,13,17,19

51.The prime factors of 36 are
(A) 2 3 4 7
(B) 2 2 3 3
(C) 2 5 6 7
(D) 1 2 3 4

52.If 21 divided by 3 then we have quotient …..
(A) prime number
(B) even number
(C) integer
(D) 0

53.Successor of every odd number is:
(A) Odd
(B) Even
(C) Irrational
(D) Integer

54.The numbers which are multiple of 2 are called
(A) Odd number
(B) Even number
(C) Integers
(D) None

55.Which number is not factor of 9?
(A) 5
(B) 3
(C) 1
(D) None

56.Predecessor of 8 is:
(A) An even number
(B) An odd number
(C) A prime number
(D) Both an odd and a prime number

57.All the factors of 25 are:
(A) 1, 5, 25
(B) 1, 5, 15
(C) 1, 5, 20
(D) 1, 2, 4

58.The H.C.F of 35, 42 and 77 is……
(A) 7
(B) 6
(C) 5
(D) 2

2M

59.Find the pair of numbers which are co-prime and twin-prime.
(a) (41, 43)
(b) (49, 51)

60.Find the prime factors of 96.

61.Find the first five multiples of 7.

62.Find all possible factors of 64.

63.Which of the following numbers are prime
(i) 89
(ii) 127

3M

64.Without doing actual division, check the divisibility of 376948 with 11.

65.Find the first three common multiples of 6 and 8

66.Find the H.C.F of 96, 128

67.Find the divisibility ofthe number 390612by 3 and 9 .

68.Find the L.C.M of 112, 160 and 188 by division method

5M

69.Check whether 438750 is divisible by 2, 4, 5, 8, 10. Give Reasons.

70.Find the least five-digit number, which leaves remainder 9 in each case when divided by 20, 40, 75

71.The length, breadth and height of a hall are 3675 cm, 2100cm and 1050 cm respectively.
What can be the maximum length of a tape with which we can measure the length ,breadth and height of the hall?

72.Find the smallest number of 4 digits which is divisible by 6, 8, 9

Q1.Write all the factors of following numbers
i) 64
ii) 86
iii) 94
iv) 17
v) 112

Q.2. Write first 8 multiples of
a) 7
b) 12
c) 16
d) 19

Q.3. Write all the prime numbers less than 25.

Q.4. Find common factors of
a) 75, 60 & 210
b) 72 & 80
c) 18, 24 & 30
d) 30,45 & 75

Q.5. Find first 6 common multiplies of
a) 2, 3 & 5
b) 3, 4 & 9
c) 5 & 7

Q.6. Write the prime factorization of
a) 60
b) 880
c) 1220

Q.7. Find HCF of
a) 12, 15 & 30
b) 36 & 45
c) 18, 54 & 81
d) 49, 91 & 112

Q.8. Find LCM of

a) 12 & 18
b) 20, 24 & 45
c) 16 & 24
d) 20, 25 & 30

I) Fill in the blanks :

1. _______________________ is a factor of every number.

2. The factor of a prime number is _____________________ and _______________.

3. A number which has more than two factor is called _____________________.

4. The smallest perfect number is ________________.

5. If a number ends with 0, it is divisible by _________________.

6. The sum of all the factors of a perfect number is equal to _______________ the number.

7. _______________ is neither prime nor composite.

8. A number is divisible by 6, if it is divisible by both ________ and _______________.

9. The smallest even numbers is ______________ and the smallest odd numbers is a ___________________.

10. Sum of any two even numbers is _______________________.

11. Sum of two odd numbers is ______________________.

12. The only one even prime is __________________________.

13. The greatest two digit prime number is __________________________.

14. The smallest two digit prime numbers is _____________________________.

15. The difference between two twin prime is ________________________.

16. A prime number has only __________________ factors.

17 . ____________________ is the unique number.

18. The smallest digit in the blank space of _____9853. So that the number so formed is divisible by 3.

19. The L.C.M of two numbers in which one is a factor of the other is ___________________________.

20. The L.C.M of two co-prime numbers ________________________.

21. The smallest factor of 856 is __________________________.

22. The smallest multiple of 856 is _____________________.

23. The greatest factor of 856 is _____________________.

24. The perfect numbers below 100 are ________________ and _________________.

25. The smallest prime number is ______________________________.

26. The smallest composite number is ____________________________.

27. The smallest number having three different prime factors is ________________.

28. The sum of any two consecutive odd numbers is always divisible by _______.

29. The product of three consecutive numbers is divisible by _____________.

Do the following :

1. Express the smallest 5 – digit number in the form of prime factor.

2. Determine if 9130 is divisible by 110.

3. Using divisibility test check whether the following are divisible by

2, 3, 4, 5, 6, 8, 9, 10 and 11
(a) 91800 (b) 31956 (c) 81615 (d) 61042 (e) 48400 (f) 99909

4. Write all the twin primes below 100.

5. Write all the prime numbers below 70.

6. Find the smallest number when divided by 28, 40 and 44 leave a remainder 8 in each case.

7. Write two prime numbers whose sum is 100.

8. Write three pairs of prime numbers whose sum is an odd number.

9. Find the smallest four digit number which is exactly divisible by 12, 16, 24 and 36.

10. Write all the composite numbers between 30 and 50.

11. The length , breadth and height of a room are 8m25cm, 6m75cm and 4m50cm respectively. Determine the longest tape which can measure the three dimension of the room exactly.

12. Telegraph pole occurs at equal distances of 220m along a road and heaps of stones are put at equal distances of 300m along the same road. The first heap is at the foot of the first pole. How far from it along the road is the next heap which lies at the foot of a pole.

I) Choose the correct answers :

1. HCF of two consecutive even numbers
a) 1
b) 2
c) 3
d) 4

2. LCM of two Prime numbers is
a) their sum
b) their difference
c) their product
d) none of these.

3. The Prime factorization of 126 is
a) 2 2 3 6
b) 2 3 37
c) 2 3 34
d) none of these

4. The fundamental theorem of Arithmetic states that :
a) every number greater than 1 has many factors.
b) every number greater than 1 has exactly one Prime factorization.
c) every number greater than 1 has many multiples.
d) none of these

5. The number which is divisible by 9 is
a) 7802
b) 8100
c) 3271
d) none of these

II) Find the value of
a) 4 + 3 (5 + 3)
b) 6 8 255 +3
c)12 (4 +2) 3 5 +7(3+1)

III) Simplify :
a) 125 [18{28 4(18305)2}]
b) 5[18 +{3+4(52)}]
c)130[100(2 of 5){8}]

IV) Using divisibility tests, determine which of the following number are divisible by 2,3,4,5,6,8 and 9.
a) 14560
b) 726352
c) 12159
d) 12150
e) 639210

V)Determine HCF of numbers given below by Prime factorization method.
a) 36, 84
b) 34, 102
c) 27,63

VI) Determine HCF of numbers given below by continued division method.
a) 28, 36
b) 880, 1375
c) 255, 1620

VII) Determine LCM of
a) 16, 24, 40
b) 18, 24, 32
c) 32, 56, 46

VIII) Write the numerical expression for each of the following using brackets :
a) Nine subtracted from the product eight and seven.
b) Seventy two divided by the sum of six and three.
c) Four multiplied by the sum of two and five.

IX. 1) Express 71 as the sum of three odd primes.
2) Express 24 as the sum of twin Primes.
3) Find all Prime numbers between 70 and 90.

X. 1) Find the least number which when divided by 6,15 and 18 leave remainder 5 in each case.
2) Find the least number which divided by 12, 16, 24 and 36 leave. remainder 7 in each case
3) Find the greatest number which divides 1,628 1,736 and 268 leaving remainders 8, 11 and 13 respectively.
4) Find the largest number which divides 146, 254 and 272 leaving a remainder 2 in each case.
5) Find the smallest 4 digit number which is divisibly by 18,24 and 32.
6) Write the smallest 5 – digit number and find its factors.
7) For each of the following pair of numbers , verify that
LCM HCF = Product of the numbers.
(i) 21, 28
(ii) 231 and 273
(iii) 36, 90

Playing With Numbers

I. Fill in the blanks

1. The value of 6 x 45 ÷ 9+3 is -----------------.

2. The numerical expression for six multiplied by the sum if three and four is ----------------

3. The numerical expression for seven subtracted from the product of four and three is

4. Numerical expression for forty five divided by the difference of eight and three is

5. The number of factors of a number are ------------ and multiples of a number are ----- .

6. Two consecutive odd prime numbers are known as -------------- .

7. A set of three consecutive prime numbers differing by 2 is called a -------

8. Two numbers are said to be ------------ if they do not have a common factor other than 1.

9. The smallest composite number is -------------.

10. HCF of two prime numbers is ------------ .

11. HCF of two consecutive even numbers is ------------ .

12. LCM of two prime consecutive numbers is ------------ .

13. LCM of two consecutive numbers is ------------ .

14. ----------- is neither a prime number nor a composite number.

15. A number for which sum of all its factors is equal to twice the number is called a --------

II.DO THE FOLLOWING

1. Find the value of a) 63 ÷ (4+7) (b) 17 +24 ÷ 6 - 3
c) 4 x 3 – 20 ÷ 5 +8 (d) 25 – 27 ÷ (6 +3)

2. Simplify:- __
a) 35 + {16 -7 +(3+5) } b) 148 – [150 ÷ 3 of 5 – { 20- 9-3} ]
c) 6 [ 24 + {4 + 3( 6 -2 )} ]

3. Write all prime numbers between1 and 50.

4. Express the following as the sum of twin primes a) 84 b) 36 c) 24 d) 42

5. Express the following as the sum of two odd primes a) 36 b)68 c) 24 d) 42

6. Using divisibility test check whether the following are divisible by 4 and 8.

7. Test the divisibility by 6 a) 27840 b) 29400 c) 35684

8. In each of the following fill in the blank with the smallest digit to make it divisible by 3.
a) 643 -5
b) 2134 -7
c) 39821-7

9) Fill in the blank with the smallest digit to make it divisible by 9.
a) 563 – 3
b) 1679 – 1
c) 23 -523

10. Write the smallest 5 digit number and find its prime factors

11. Determine the HCF of the given numbers by prime factorisation method.
a) 72, 120
b) 46, 78
c) 225, 350

12. The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

13. Determine the HCF by continued division method.
a) 255, 1620
b) 880, 1375
c) 72, 126

14.Find the largest number which divides 226 and 311 leaving a reminder of 5 in each case.

15.For each of the following pairs of numbers verify that:LCM x HCF = Product of the numbers.
a) 231,273
b) 104, 195
c) 36, 90

16. Find the smallest number which when divided by 15, 25 and 35 leaves a remainder 5 in each case.