CBSE Class 5 Mathematics Factors And Multiples Worksheet Set E

Topic : Factors and Multiples

Least Common Multiple ( LCM )- The LCM of two or more given numbers is the smallest multiple of each of the given numbers.
For Example : Let the numbers 6 and 8.
The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48 ………………………………
The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64 ……………………………….
Common multiple of 6 and 8 are 24 , 48 ……………..
The least common multiple of 6 and 8 is 24.
Hence LCM of 6 and 8 are 24.

NOTE - ALL QUESTIONS ARE COMPULSORY.

Find the LCM by using prime factorization method :

(1) 18 and 24 .

(2) 63 and 105 .

(3) 28 , 56 and 84 .

(4) 27 , 54 and 90 .

Find the LCM by using short division method :

(5) 16 and 24 .

(6) 32 and 48 .

(7) 28 , 42 and 56 .

Q.1 Write4pairsoftwinprimes.

Q.2. Write4pairsofcoprimes

Q.3. Find the H.C.F. Of the following numbers by using the prime factorisation method.:-
a. 144,180,384.
b. 106,159,371

Q.4. Find the H.C.F. Of the following numbers by using the division method
a. 170&255.
b. 1050,750&425

Q.5. Find the L.C.M. Of the following numbers by using the prime factorisation method:-
a. 112,168,266.
b. 144,180,384.

Q.6. Find the L.C.M. Of the following numbers by using the prime division method
a. 22,54,108,135&198
b. 28,36,45,60

Question. Find the odd one out.
(a) 15
(b) 21
(c) 27
(d) 31
Answer : D

Question. Which of the following represents the complete factor tree for 84?

Answer : A

Question. The number of factors of 126 are _______. 
(a) 12
(b) 14
(c) 16
(d) 18
Answer : A

Question. In how many different ways we can arrange 24 glasses on a kitchen shelf ? Choose the best answer.
(a) 4 ways
1. All 24 glasses in 1 row.
2. 2 rows of 12 glasses each.
3. 3 rows of 8 glasses each.
4. 4 rows of 6 glasses each.
(b) 3 ways
1. All glasses in 1 row.
2. 2 rows of 12 glasses each.
3. 3 rows of 8 glasses each.
(c) 2 ways
1. All glasses in 1 row.
2. 3 rows of 8 glasses each.
3. 4 rows of 6 glasses each.
(d) 1 way
1. All glasses in 1 row.
Answer : A

Question. Sum of factors of 71 is _______.
(a) 72
(b) 194
(c) 71
(d) 78
Answer : A

Question. Match the following :

     A      B     C      D
(a) 4      1      2      3
(b) 4      1      3      2
(c) 1      4      2      3
(d) 4      3      2      1
Answer : A

Question. The greatest number that will divide 37, 50, 123 leaving remainder 1, 2 and 3 respectively is :
(a) 9
(b) 10
(c) 15
(d) 12
Answer : D

Question. Which of the following statements are true or false.
(A) If a number is divisible by 6, it must be divisible by 12.
(B) If a number is divisible by 6, it must be divisible by 3.
(C) If a number is divisible by 100, it must be divisible by 25.
(D) A number divisible by 256 is even.
(a) FTFT
(b) FTTT
(c) TFTT
(d) TTFT
Answer : B

Question. The greatest number that will divide 137, 182 and 422 leaving a remainder of 2 in each case is :
(a) 15
(b) 12
(c) 21
(d) none of these
Answer : A

Directions (Qs. a to e) : Read the passage and complete it by choosing the correct option.
A number is divisible by ___(30)___ if it has 0 or an even number in its ones place. A number is divisible by 3 if the ___(31)___ of its digits is divisible by 3. A number is divisible by 5 if it has ___(32)___ or 5 in its ones place. A number is divisible by ___(33)___ if it is divisible by both 3 and 5. A number is divisible by another number if it is also divisible by its ___(34)___ factors.

Question a.
(a) 2
(b) 3
(c) 4
(d) 6
Answer : A

Question b.
(a) sum
(b) product
(c) difference
(d) division
Answer : A

Question c.
(a) 0
(b) 1
(c) 10
(d) 2
Answer : A

Question d.
(a) 15
(b) 3
(c) 5
(d) 10
Answer : A

Question e.
(a) co-prime
(b) prime
(c) each
(d) others
Answer : A

Question. The smallest 4-digit number exactly divisible by 12, 15, 20 and 35 is _______.
(a) 1,000
(b) 1,160
(c) 1,260
(d) none of these
Answer : C

Question. List the prime factorization of 24:
(a) 2 × 2 × 2 × 3
(b) 3 × 2 × 4
(c) 3 × 8
(d) 12 × 2
Answer : A

Question. Add the 4th multiple of 52 and the 8th multiple of 37. The value obtained is 700 less than ♣. Find ♣.
(a) 1400
(b) 1004
(c) 968
(d) 1204
Answer : D

Question. Find the GCF of 15 and 6:
(a) 5
(b) 6
(c) 3
(d) 2
Answer : C

Question. The difference between the (sum of third multiple of 18 and the sixth multiple of 12) and sum of factors of 24 is ______. 
(a) 66
(b) 186
(c) 176
(d) 126
Answer : A

Question. What is the greatest common factor (GCF) of 42 and 72?
(a) 2 + 2/3
(b) 3
(c) 6
(d) 9
Answer : C

Question. Look at the calendar. What best describes the dates that are on Saturdays?

(a) Multiples of 2
(b) Multiples of 3
(c) Multiples of 4
(d) Multiples of 7
Answer : D

Question. Which of the following pairs of numbers have a least common multiple (LCM) of 56?
(a) 2 and 28
(b) 7 and 8
(c) 4 and 14
(d) 3 and 17
Answer : B

Question. Girish is making a math puzzle. He writes that ‘w’ is an even number which has 12 as a factor. Which of the following could represent the variable ‘w’? 
(a) 2156
(b) 1728
(c) 1429
(d) 1256
Answer : B

Question. Which two numbers do not have 11 as their greatest common factor?
(a) 22 and 44
(b) 33 and 55
(c) 11 and 101
(d) 33 and 99
Answer : C

Question. Which one of the following digits should be placed in the middle of the digits of the number 258970 so that 3 becomes factor of it?
(a) 0
(b) 1
(c) 2
(d) 3
Answer : C

Question. A number that has more factors than one and itself. Or, a number that has more than two factors. For example: 8 has factors 1 and 8, but it also has factors 2 and 4.
(a) Prime number
(b) Composite number
(c) Factor number
(d) Multiple number
Answer : B

1. Which two numbers are factors of 24?
a) 6 and 5
b) 7 and 6
c) 4 and 6

2. Which is a factor of 20?
a) 4
b) 8
c) 3

3. Which two numbers are factors of 44?
a) 11 and 3
b) 5 and 7
c) 4 and 11

4. Which number is a multiple of 12?
a) 36
b) 34
c) 42

5. Choose all that apply, the number 52 is ?
1. even
2. odd
3. prime
4. composite
5. square

6. A composite number is
1. A number that creates other numbers.
2. Always last.
3. A number which has factors other than 1 and itself.

7. The prime factorization of 48 is
1. 2 x 2 x 2 x 2 x 3
2. 2 x 2 x 2 x 3
3. 2 x 3 x 2 x 4

8. What are the divisibility factors for 36?
• 1,2,3,4,9,12,18,36
• 1,2,3,4,6,9,12,18,36
• 3,2,3,3

9. Everyday there is atleast 2 special dishes in a restaurant. If burger is in the menu on every sixth day and pizza is served every eighth day and both pizza and burger are on today’s menu, how many days will it be that they are both on the menu again.

10. For a musical concert, 30 chairs are needed to be arranged. List all the possible ways the chairs can be arrange.

Topic : Factors and Multiples

Factors and Multiples : When a number divides another number exactly, then the divisor is called a factor of the dividend , and, the dividend is called a multiple of the divisor.
For Example : We know that 4 divides 20 exactly.
4 is a factor of 20, and 20 is a multiple of 4 .
Example 1 : (a) All factors of 4 are 1 , 2 , 4.
(b) All factors of 8 are 1 , 2 , 4 , 8.
(c) All factors of 16 are 1 , 2 , 4 , 8 16.
Example 2: (a) First five multiples of 3 are 3, 6, 9, 12, 15 .
(b) First five multiple of 7 are 7, 14, 21, 28, 35.

Properties of Factors :
• 1 is a factor of every number.
• Every non zero number is a factor of itself.
• A factor is a non zero number is less than or equal to the number .
• 1 is the only number having one factor, namely itself.
• Every non zero number other than 1 has at least two factors, namely 1 and itself.
• Every non zero number is a factor of 0(zero) .

Properties of multiples :
• Every number is a multiple of 1.
• Every number is a multiple of itself.
• Every non zero multiple of a non zero number is greater than or equal to the number.
• We can find many multiples of a non zero number.
• 0 is a multiple of every number.

NOTE - ALL QUESTIONS ARE COMPULSORY.
(1) Write the first five multiples of 4 .
(2) Write the first six multiples of 9 .
(3) Write the first four multiples of 12 .
(4) Write the first five multiples of 25 .
(5) Write the first five multiples of 16.
(6) Write all the factors of 12.
(7) Write all the factors of 24 .
(8) Write all the factors of 28 .
(9) Write all the factors of 60 .
(10) Write all the factors of 45 .

Q1 Write all the factors of

(a) 28- _____, _____, ______, _____, ______, ______

(b) 45- ______, ______, ______, ______, ______, ______

(c) 36- ______, ______, ______, _______, ______, ______, ______, ______, ______

Q2 Find the HCF of the following numbers:
(a) 35,45 (b) 24,66

Q3 Find the LCM of the following numbers:
(a) 8,16,48 (b) 10,20

Q4 Write the next three multiples of:

(a) 12- 12, 24, 36, _______, _______, _______

(b) 17- 17, 34, 51, _______, _______, ______

Topic : Factors and Multiples

(6) Test of divisibility by 8: A number is divisible by 8, if the number formed by its last 3 digits on its extreme right is divisible by 8.
For example: Let the number 279136.
The number formed by its last three digits is 136 , which is divisible by 8.
Hence 279136 is divisible by 8.

(7) Test of divisibility by 9: A number is divisible by 9, if the sum of its digits is divisible by 9.
For example: Let the number be 8316.
Sum of digits = 8+3+1+6 = 18 , which is divisible by 9.
Hence 8316 is divisible by 9.

(8) Test of divisibility by 10: A number is divisible by 10 only when its unit digit is only 0.
For example: The numbers 2560 , 17340 and 962020 has 0 as its unit digit.
Hence each one is divisible by 10.

(9) Test of divisibility by 11: A number is divisible by 11, if the difference between the sum of digits at odd places and the sum of digits at even places is either 0 or a multiple of 11.
For example: Check the number 32571 is divisible by11.
Sum of its digits at odd places = 1 + 5 + 3 = 9
Sum of its digits at even places = 7 + 2 = 9
Their difference = 9 ̶ 9 = 0
Hence given number is divisible by 11.

Prime Numbers: A number having exactly two different factors , 1 and itself is called a prime number.
For example : Prime numbers are 2 , 3 , 5 , 7 , 11 , 13 , 17 etc .

Composite Numbers: A number having more than two different factors is called a composite number.
For Example : Composite numbers are 4 , 6 , 8 , 9 , 12 , 14 etc .

Note :
• 1 is neither prime nor composite .
• The smallest prime number is 2 .
• 2 is only even prime number .

NOTE - ALL QUESTIONS ARE COMPULSORY.

(1) Which of the following numbers are divisible by 6 ?
(a) 8316 (b) 9430 (c) 7038 (d) 17703 (e) 8721

(2) Which of the following numbers are divisible by 8 ?
(a) 1372 (b) 62156 (c) 50432 (d) 59238 (e) 279136

(3) Which of the following numbers are divisible by 9 ?
(a) 7509 (b) 4186 (c) 26901 (d) 12501 (e) 3499

(4) Which of the following numbers are divisible by 10 ?
(a) 1980 (b) 1850 (c) 3206 (d) 9910 (e) 27905

(5) Which of the following numbers are divisible by 11 ?
(a) 75438 (b) 623411 (c) 20833 (d) 101011 (e) 202202

(6) Which of the following numbers are prime numbers ?
1 , 11 , 21 , 57 , 63 , 19 , 91 , 83 and 89 .

(7) Which of the following numbers are composite numbers ?
1 , 4 , 7 , 12 , 22 , 34 , 81 , 93 , 100 and 111.

(8) Write all the prime numbers between 1 and 25.

(9) Write all the prime numbers between 51 and 80.

(10) Define Prime and Composite numbers.