Exercise 3.1
Question 1: Write down the smallest natural number.
Solution 1: The Smallest natural number is ‘1’.
Question 2: Write down the smallest whole number.
Solution 2: The Smallest whole number is ‘0’.
Question 3: Write down, if possible, the largest natural number.
Solution 3: As we know that every Natural number has a successor Number. So, there is not the largest Natural Number.
Question 4: Write down, if possible, the largest whole number.
Solution 4: As we know that every whole number has a successor Number. So, there is not the largest Whole Number.
Question 5: Are all natural numbers also whole numbers?
Solution 5: Yes, all the natural numbers also the whole numbers.
Question 6: Are all whole numbers also natural numbers?
Solution 6: No, all the whole numbers are not the natural numbers because ‘0’ is not a Natural number but it is a Whole Number
Question 7: Give successor of each of the whole numbers?
(i) 1000909
(ii) 2340900
(iii) 7039999
Solution 7:
(i) 1000909 = 1000909 + 1 = 1000910
Successor of 1000909 is 1000910.
(ii) 2340900 = 2340900 + 1 = 2340901
Successor of 2340900 is 2340901.
(iii) 7039999 = 7039999 + 1 = 7040000
Successor of 7039999 is 7040000.
Question 8: Write down the predecessor of each of the following whole numbers:
(i) 10000
(ii) 807000
(iii) 7005000
Solution 8:
(i) 10000 = 10000 - 1 = 9999
Predecessor of 10000 is 9999.
(ii) 807000 = 807000 - 1 = 806999
Predecessor r of 807000 is 806999.
(iii) 7005000 = 7005000 - 1 = 7004999
Predecessor of 7005000 is 7004999.
Question 9: Represent the following numbers on the number line:
2,0,3,5,7,11,15
Solution 9:
Numbers are as shown in the above line.
Question 10: How many whole numbers are there between 21 and 61?
Solution 10: There are 39 whole number between 21 and 61.
Question 11: Fill in the blanks with the appropriate symbol < or >:
(i) 25______205
(ii) 170______107
(iii) 415______514
(iv) 10001______100001
(v) 2300014______2300041
Solution 11:
(i) 25 < 205
(ii) 170 > 107
(iii) 415 > 514
(iv) 10001 < 100001
(v) 2300014 < 2300041.
Question 12: Arrange the following numbers is descending order:
925, 786, 1100, 141, 325, 886, 0, 270
Solution 12:
Descending Series:
1100, 925, 886, 786, 325, 270, 141, 0.
Question 13: Write the largest number of 6 digits and the smallest number of 7 digits. Which one of these two is larger and by how much?
Solution 13:
Largest 6-digit number is: 999999
Smallest 7-digit number is: 1000000
The larger Number is 1000000 by 1
Question 14: Write down three consecutive whole numbers just preceding 8510001.
Solution 14:
First Number: 8510001- 1 = 8510000,
Second Number: 8510000 – 1 = 8509999,
Third Number: 8509999- 1 = 8509998.
Preceding Numbers:
8510000, 8509999, 8509998.
Question 15: Write down the next three consecutive whole numbers starting from 4009998.
Solution 15:
First Number: 4009998 + 1 = 4009999,
Second Number: 4009999 + 1 = 4010000,
Third Number: 4010000 + 1 = 4010001.
Successive Numbers:
4009999, 4010000, 4010001.
Question 16: Give arguments in support of the statement that there does not exist the largest natural number.
Solution 16: Every natural number has its successes. Therefore, the largest natural number does not exist.
Question 17: Which of the following statements are true and which are false?
Solution 17:
Every whole number has its successor. True
Every whole number has its predecessor. False
0 is the smallest natural number. False
1 is the smallest whole number. False
0 is less than every natural number. True
Between any two whole numbers there is a whole number. False
Between any two non-consecutive whole numbers there is a whole number. True
The smallest 5-digit number is the successor of the largest 4 digit number True
Of the given two natural numbers, the one having more digits is greater. True
The predecessor of a two digit number cannot be a single digit number. False
If a and b are natural numbers and a < b, than there is a natural number c such that a<b<c. False
If a and b are whole numbers and a<b, then a+1< b+1. True
The whole number 1 has 0 as predecessor. True
The natural number 1 has no predecessor. True
Objective Type Questions
Mark the correct alternative in each of the following:
Question 1: The smallest natural number is
(a) 0
(b) 1
(c) -1
(d) None of these
Solution 1: (b) 1 is the smallest natural number.
Question 2: The smallest whole number is
(a) 1
(b) 0
(c) -1
(d) None of these
Solution 2: (b) 0 is the smallest whole number.
Question 3: The predecessor of 1 in natural numbers is
(a) 0
(b) 2
(c) -1
(d) None of these
Solution 3: (d) 1 is the smallest natural number and it does not have any predecessor.
Question 4: The predecessor of 1 in whole numbers is
(a) 0
(b) -1
(c) 2
(d) None of these
Solution 4: (a)
Predecessor of 1 is
= 1 – 1
= 0.
Question 5: The predecessor of 1 million is
(a) 9999
(b) 99999
(c) 999999
(d) 1000001
Solution 5: (c)
1 million = 10, 00,000
= 10, 00,000 – 1
= 9, 99,999
Question 6: The successor of 1 million is
(a) 10001
(b) 100001
(c) 1000001
(d) 10000001
Solution 6: (c)
1 million = 10, 00,000
= 10, 00,000 + 1
= 10, 00,001
Question 7: The product of the successor and predecessor of 99 is
(a) 9800
(b) 9900
(c) 1099
(d) 9700
Solution 7: (a)
The successor of 99
= 99 + 1
= 100
Predecessor of 99
= 99 − 1
= 98
Product of successor and predecessor = 100 × 98 = 9800
Question 8: The product of a whole number (other than zero) and its successor is
(a) an even number
(b) an odd number
(c) divisible by 4
(d) divisible by 3
Solution 8: (a)
Let the whole number is = 3
The successor of 3 = 3 + 1 = 4
Product between them = 3 × 4 = 12
Hence, 12 is an even number.
Question 9: The product of the predecessor and successor of an odd natural number is always divisible by
(a) 2
(b) 4
(c) 6
(d) 8
Solution 9: (b)
Question 10: The product of the predecessor and successor of an even natural number is
(a) divisible by 2
(b) divisible by 3
(c) divisible by 4
(d) an odd number
Solution 10: (d)
Let an even natural number = 4
The predecessor of 4 = 4 − 1 = 3
The successor of 4 = 4 + 1 = 5
Product between them = 3 × 5 = 15
Thus, the product is an odd number.
Question 11: The successor of the smallest prime number is
(a) 1
(b) 2
(c) 3
(d) 4
Solution 11: (c)
The smallest prime number is 2
The Successor of 2 = 2 + 1
= 3
Question 12: If x and y are co-primes, then their LCM is
(a) 1
(b) x/y
(c) xy
(d) None of these
Solution 12: (c)
The LCM of x and y is
Question 13: The HCF of two co-primes is
(a) the smaller number
(b) the larger number
(c) product of the numbers
(d) 1
Solution 13: (d)
The HCF of two co-prime numbers is 1.
Question 14: The smallest number which is neither prime nor composite is
(a) 0
(b) 1
(c) 2
(d) 3
Solution 14: (b)
1 is the only smallest natural number which is neither prime nor composite.
Question 15: The product of any natural number and the smallest prime is
(a) an even number
(b) an odd number
(c) a prime number
(d) None of these
Solution 15: (a)
The smallest prime number is 2.
Thus, multiplied by any natural number we get an even number.
Question 16: Every counting number has an infinite number of
(a) factors
(b) multiples
(c) prime factors
(d) None of these
Solution 16: (b)
Every counting number has an infinite number of multiples.
Question 17: The product of two numbers is 1530 and their HCF is 15. The LCM of these numbers is
(a) 102
(b) 120
(c) 84
(d) 112
Solution 17: (a)
Product of two numbers = HCF × LCM
1530 = 15 × LCM
1530/15 = LCM
102 = LCM
Thus, the LCM of two numbers 102.
Question 18: The least number divisible by each of the numbers 15, 20, 24 and 32 is
(a) 960
(b) 480
(c) 360
(d) 640
Solution 18: (b)
We know that the LCM of 15, 20, 24 and 32 is
Prime Factorization of 15 is = 3 × 5
Prime Factorization of 20 is = 2 × 2 × 5
Prime Factorization of 24 is = 2 × 2 × 2 × 3
Prime Factorization of 32 is = 2 × 2 × 2 × 2 × 2
Thus, the LCM = 2 × 2 × 2 × 2 × 2 × 3 × 5 = 480
Question 19: The greatest number which divides 134 and 167 leaving 2 as remainder in each case is
(a) 14
(b) 19
(c) 33
(d) 17
Solution 19: (c)
Subtract the remainder from given number
134 – 2 = 132
167 – 2 = 165
LCM of 132 and 165
Prime Factorization of 132 is = 2 × 2 × 3 × 11
Prime Factorization of 165 is = 3 × 5 × 11
HCF = 3 × 11 = 33
Thus, the greatest number which divides 134 and 167 leaving 2 as remainder is 33.
Question 20: Which of the following numbers is a prime number?
(a) 91
(b) 81
(c) 87
(d) 97
Solution 20: (d)
Prime Factorization of 91 is = 1 × 7 × 13
Prime Factorization of 81 is = 1 × 3 × 3 × 3 × 3
Prime Factorization of 87 is = 1 × 3 × 29
Prime Factorization of 97 is = 1 × 97
Thus, the prime numbers is 97.
Question 21: If two numbers are equal, then
(a) their LCM is equal to their HCF
(b) their LCM is less than their HCF
(c) their LCM is equal to two times their HCF
(d) None of these
Solution 21: (a)
If two numbers are equal, then
HCF = LCM
Question 22: a and b are two co-primes. Which of the following is/are true?
(a) LCM (a, b) = a × b
(b) HCF (a, b) = 1
(c) Both (a) and (b)
(d) Neither (a) nor (b)
Solution 22: (c)
LCM and product of two co-prime numbers are equal.
Hence, the HCF of two co-prime numbers is 1.