Chapter - 3 - EXERCISE 3.2 - Playing with Numbers (NCERT Class 6th Maths Solution)
1. What is the sum of any two :
(a) Odd numbers? (b) Even numbers?
Solution/Explanation:
(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 =14
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.
Solution/Explanation:
(a) The sum of three odd numbers is even.False
3 + 5 + 7 = 15. i,e. odd
(b) The sum of two odd numbers and one even number is even.True
3 + 5 + 6 = 14 i,e = even
(c) The product of three odd numbers is odd. True
3 × 5 × 7 = 105 i.e, odd.
(d) If an even number is divided by 2, the quotient is always odd. False
4 ÷ 2 = 2 i.e, even
(e) All prime numbers are odd.False
2 is even number.
(f) Prime numbers do not have any factors. False
1 and the numbers itself are factors of the number.
(g) Sum of two prime numbers is always even. False
2 + 3 = 5 i,e odd
(h) 2 is the only even prime number.True
(i) All even numbers are composite numbers. False
2 is a prime numbers.
(j) The product of two even numbers is always even.True
2 × 4 = 8, i.e 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 upto 100.
Solution/Explanation:
17 and 71
37 and 73
79 and 97
4. Write down separately the prime and composite numbers less than 20.
Solution/Explanation:
Composite numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18
5. What is the greatest prime number between 1 and 10?
Solution/Explanation:
Prime numbers between 1 and 10 are 2, 3, 5, and 7. Among these numbers, 7 is the greatest.
6. Express the following as the sum of two odd primes.
(a) 44 (b) 36 (c) 24 (d) 18
Solution/Explanation:
(a)44=37+7
(b)36=23+13
(c)24=19+5
(d)18=11+7
7. Give three pairs of prime numbers whose difference is 2. [Remark : Two prime numbers whose difference is 2 are called twin primes].
Solution/Explanation:
Three pairs of prime numbers whose difference is 2 are as follows.
1) 3 and 5
2) 11 and 13
3) 17 and 19
8. Which of the following numbers are prime?
(a) 23 (b) 51 (c) 37 (d) 26
Solution/Explanation:
9. Write seven consecutive composite numbers less than 100 so that there is no prime number between them.
Solution/Explanation:
10. Express each of the following numbers as the sum of three odd primes:
(a) 21 (b) 31 (c) 53 (d) 61
Solution/Explanation:
(a)
(b)
(c)
(d)
11. Write five pairs of prime numbers less than 20 whose sum is divisible by 5. (Hint : 3+7 = 10)
Solution/Explanation:
2 + 3 = 5
7 + 13 = 20
3 + 17 = 20
2 + 13 = 15
5 + 5 = 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 is neither ______ nor ______.
(d) The smallest prime number is ______.
(e) The smallest composite number is _____.
(f) The smallest even number is ______.
Solution/Explanation:
(a) A number which has only two factors is called a Prime number.
(b) A number which has more than two factors is called a composite number .
(c) 1 is neither composite nor prime number.
(d) The smallest prime number is 2.
(e) The smallest composite number is 4.
(f) The smallest even number is 2.
(a) The sum of three odd numbers is even.False
3 + 5 + 7 = 15. i,e. odd
(b) The sum of two odd numbers and one even number is even.True
3 + 5 + 6 = 14 i,e = even
(c) The product of three odd numbers is odd. True
3 × 5 × 7 = 105 i.e, odd.
(d) If an even number is divided by 2, the quotient is always odd. False
4 ÷ 2 = 2 i.e, even
(e) All prime numbers are odd.False
2 is even number.
(f) Prime numbers do not have any factors. False
1 and the numbers itself are factors of the number.
(g) Sum of two prime numbers is always even. False
2 + 3 = 5 i,e odd
(h) 2 is the only even prime number.True
(i) All even numbers are composite numbers. False
2 is a prime numbers.
(j) The product of two even numbers is always even.True
2 × 4 = 8, i.e 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 upto 100.
Solution/Explanation:
17 and 71
37 and 73
79 and 97
4. Write down separately the prime and composite numbers less than 20.
Solution/Explanation:
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19
Composite numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18
5. What is the greatest prime number between 1 and 10?
Solution/Explanation:
Prime numbers between 1 and 10 are 2, 3, 5, and 7. Among these numbers, 7 is the greatest.
6. Express the following as the sum of two odd primes.
(a) 44 (b) 36 (c) 24 (d) 18
Solution/Explanation:
(a)44=37+7
(b)36=23+13
(c)24=19+5
(d)18=11+7
7. Give three pairs of prime numbers whose difference is 2. [Remark : Two prime numbers whose difference is 2 are called twin primes].
Solution/Explanation:
Three pairs of prime numbers whose difference is 2 are as follows.
1) 3 and 5
2) 11 and 13
3) 17 and 19
8. Which of the following numbers are prime?
(a) 23 (b) 51 (c) 37 (d) 26
Solution/Explanation:
9. Write seven consecutive composite numbers less than 100 so that there is no prime number between them.
Solution/Explanation:
Seven consecutive composite numbers less than 100 so that there is no prime number between them are :
Between 89 and 97, both of which are prime numbers, there are 7 composite numbers. They are: 90,91,92,93,94,95,96
(a) 21 (b) 31 (c) 53 (d) 61
Solution/Explanation:
(a)
(b)
(c)
(d)
11. Write five pairs of prime numbers less than 20 whose sum is divisible by 5. (Hint : 3+7 = 10)
Solution/Explanation:
2 + 3 = 5
7 + 13 = 20
3 + 17 = 20
2 + 13 = 15
5 + 5 = 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 is neither ______ nor ______.
(d) The smallest prime number is ______.
(e) The smallest composite number is _____.
(f) The smallest even number is ______.
Solution/Explanation:
(a) A number which has only two factors is called a Prime number.
(b) A number which has more than two factors is called a composite number .
(c) 1 is neither composite nor prime number.
(d) The smallest prime number is 2.
(e) The smallest composite number is 4.
(f) The smallest even number is 2.
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