Class 6 NCERT Solutions - Playing With Numbers

1. Write all the factors of the following numbers: (a) 24 (b) 15 (c) 21 (e) 12 (f) 20 (g) 18 (i) 36

2. Write first five multiples of: (a) 5 (b) 8  (c) 9
 
3. Find all the multiples of 9 up to 100. 
  
Answers. 
  
1.
 (a) 24 = 1 x 24 = 2 x 12 = 3 x 8 = 4 x 6 = 6 x 4
∴ Factors of 24 = 1, 2, 3, 4, 6, 12, 24 (b) 15 = 1 x 15 = 3 x 5 = 5 x 3
∴ Factors of 15 = 1, 3, 5, 15 (c) 21 = 1 x 21 = 3 x 7 = 7 x 3
∴ Factors of 21 = 1, 3, 7, 21 (d) 27 = 1 x 27 = 3 x 9 = 9 x 3
∴ Factors of 27 = 1, 3, 9, 27 (e) 12 = 1 x 12 = 2 x 6 = 3 x 4 = 4 x 3
∴ Factors of 12 = 1, 2, 3, 4, 6, 12 (f) 20 = 1 x 20 = 2 x 10 = 4 x 5 = 5 x 4
∴ Factors of 20 = 1, 2, 4, 5, 10, 20 (g) 18 = 1 x 18 = 2 x 9 = 3 x 6
∴ Factors of 18 = 1, 2, 3, 6, 9, 18 (h) 23 = 1 x 23
∴ Factors of 23 = 1, 23 (i) 36 = 1 x 36 = 2 x 18 = 3 x 12 = 4 x 9 = 6 x 6
∴ Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 3. 

2.
 (a) 5 x 1 = 5, 5 x 2 = 10, 5 x 3 = 15, 5 x 4 = 20, 5 x 5 = 25
∴ First five multiples of 5 are 5, 10, 15, 20, 25. (b) 8 x 1 = 8, 8 x 2 = 16, 8 x 3 = 24, 8 x 4 = 32, 8 x 5 = 40
∴ First five multiples of 8 are 8, 16, 24, 32, 40. (c) 9 x 1 = 9, 9 x 2 = 18, 9 x 3 = ,27, 9 x 4 = 36, 9 x 5 = 45
∴ First five multiples of 9 are 9, 18, 27, 36, 45. 3.

3. Multiples of 9 up to 100 are:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 9. 

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Questions

1. What is the sum of any two: (a) Odd numbers. (b) Even numbers.

2. State whether the following statements are true or false:
(a) The sum of three odd numbers is even. 
(b) The sum of two odd numbers and one even number is even. 
(c) The product of three odd numbers is odd. 
(d) If an even number is divided by 2, the quotient is always odd.
(e) All prime numbers are odd. 
(f) Prime numbers do not have any factors. 
(g) Sum of two prime numbers is always even. 
(h) 2 is the only even prime number. 
(i) All even numbers are composite numbers. 
(j) The product of two even numbers is always even.

3. The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers up to 100.
4. Write down separately the prime and composite numbers less than 20.
5. What is the greatest prime number between 1 and 10?
6. Express the following as the sum of two odd numbers: (a) 44 (b) 36 (c) 24 (d) 1. 
7. Give three pairs of prime numbers whose difference is 2. [Remark: Two prime numbers whose difference is 2 are called twin primes.]
8. Which of the following numbers are prime: (a) 23 (b) 51 (c) 37 (d) 26
9. Write seven consecutive composite numbers less than 100 so that there is no prime number between them.
10. Express each of the following numbers as the sum of three odd primes: (a) 21 (b) 31 (c) 53 (d) 61
11. Write five pairs of prime numbers less than 20 whose sum is divisible by 5. [Hint: 3 + 7 = 10]
12. Fill in the blanks: (a) A number which has only two factors is called a _______________. (b) A number which has more than two factors is called a _______________. (c) 1 neither _______________ nor _______________. (d) The smallest prime number is _______________. (e) The smallest composite number is _______________. (f) The smallest even number is _______________.

Answers

1. (a) The sum of any two odd numbers is an even number.
Example: 1 + 3 = 4, 3 + 5 = 8 (b) The sum of any two even numbers is an even number.
Example: 2 + 4 = 6, 6 + 8 = 1. 

2. (a) False (b) True  (c) True (d) False  (e) False. (f) False  (g) False (h) True (i) False (j) Tru.

3.17 and 71; 37 and 73; 79 and 97

4.  Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19
Composite numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 1. 5.

5. The greatest prime number between 1 and 10 is ‘7’. 

6. (a) 3 + 41 = 44 (b) 5 + 31 = 36 (c) 7 + 17 = 24 (d) 7 + 11 = 18

7. 3 and 5; 5 and 7; 11 and 13 

8. (a) 23 and (c) 37 are prime numbers.

9. 90, 91, 92, 93, 94, 95, 96 

10. (a) 21 = 3 + 7 + 11 (b) 31 = 3 + 11 + 17 (c) 53 = 13 + 17 + 23 (d) 61 = 19 + 29 + 13

11. 2 + 3 = 5; 7 + 13 = 20; 3 + 17 = 20; 2 + 13 = 15. 

12. (a) Prime number (b) Composite number (c) Prime number and composite number (d) 2 (e) 4 (f) 2