## NCERT Exercise 3.2 solution class 6 Math Part:2

In this part of NCERT Exercise 3.2 solution part-2 the solution of question number (3) to question number 12 has been given. These questions are based on prime number, composite number, odd numbers, and even numbers. The last question number (12) is fill in the blank and based on prime, composite, even and odd numbers.

Question (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.

**Answer**

Prime numbers other than 13 and 31 upto 100 which have same digits are

17 and 71, 37 and 73, 79 and 97 **Answer**

Question (4) Write down separately the prime and composite numbers less than 20.

**Answer**

Prime Numbers less than 20 = 2, 3, 5, 7, 11, 13, and 17 **Answer**

Composite Numbers less than 20 = 4, 6, 8, 9, 10, 12, 14, 15, 16, and 18 **Answer**

Question (5) What is the greatest prime number between 1 and 10?

**Answer** The greatest prime number between 1 and 10 = 7 **Answer**

Question (6) Express the following as the sum of two odd primes.

(a) 44

**Solution**

44 = 3 + 41

44 = 5 + 39

44 = 7 + 37

44 = 13 + 31

Thus, 44 can be expressed as the sum of two odd primes in four ways which are 3 + 41, 5 + 39, 7 + 37, and 13 + 31 **Answer**

(b) 36

**Solution**

36 = 31 + 5

36 = 7 + 29

36 = 13 + 23

36 = 17 + 19

Thus, 36 can be expressed as the sum of two odd primes in four ways which are 31 + 5, 7 + 29, 13 + 23, and 17 + 19 **Answer**

(c) 24

**Solution**

24 = 5 + 19

24 = 7 + 17

24 = 11 + 13

Thus, 24 can be expressed as the sum of two odd primes in three ways which are 5 + 19, 7 + 17, and 11 + 13 **Answer**

(d) 18

**Solution**

18 = 5 + 13

18 = 7 + 11

Thus, 18 can be expressed as the sum of two odd primes in two ways which are 5 + 13 and 7 + 11 **Answer**

Question (7) Give three pairs of prime numbers whose difference is 2.

[Remark: Two prime numbers whose difference is 2 are called twin primes.]

**Solution**

Three pairs of prime numbers having whose difference is 2

= (i) 3 and 5 (ii) 5 and 7 (iii) 11 and 13 **Answer**

**Extra**

Other such prime numbers having difference of 2 between them (twin primes) up to 100 are

(i) 17 and 19 (ii) 41 and 43 (iii) 71 and 73

Thus, there are 6 twin primes upto 100 which are

(i) 3 and 5 (ii) 5 and 7 (iii) 11 and 13 (iv) 17 and 19 (v) 41 and 43, and (vi) 71 and 73

Question (8) Which of the following numbers are prime?

(a) 23 (b) 51 (c) 37 (d) 26

**Answer** (a) 23 and (c) 37 are prime numbers among the given numbers **Answer**

Question (9) Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

**Answer**

There are only seven consecutive composite number upto 10 which have no prime number between them.

These numbers are 90, 91, 92, 93, 94, 95, and 96 **Answer**

Question (10) Express each of the following numbers as the sum of three odd primes:

(a) 21

**Solution**

21 = 3 + 5 + 13

21 = 3 + 7 + 11

21 can be expresses as the sum of three odd numbers in two ways which are 3 + 5 + 13 and 3 + 7 + 11 **Answer**

(b) 31

**Answer**

31 = 3 + 5 + 23

31 = 7 + 11 + 13

31 can be expresses as the sum of three odd numbers in two ways which are 3 + 5 + 23 and 7 + 11 + 13 **Answer**

(c) 53

**Answer**

3 + 7 + 43 = 53

3 + 19 + 31 = 53

5 + 11 + 37 = 53

11 + 19 + 23 = 53

13 + 17 + 23 = 53

53 can be expresses as the sum of three odd numbers in the given five ways which are 3 + 7 + 43, 3 + 19 + 31, 5 + 11 + 37, 11 + 19 + 23, and 13 + 17 + 23 **Answer**

(d) 61

**Solution**

3 + 5 + 53 = 61

3 + 11 + 47 = 61

5 + 13 + 47 = 61

7 + 11 + 43 = 61

9 + 11 + 41 = 61

7 + 13 + 41 = 61

3 + 17 + 41 = 61

7 + 17 + 37 = 61

11 + 13 + 37 = 61

5 + 19 + 37 = 61

7 + 23 + 31 = 61

11 + 19 + 31 = 61

13 + 19 + 29 = 61

53 can be expresses as the sum of three odd numbers in the given 13 ways which are 3 + 5 + 53, 3 + 11 + 47, 5 + 13 + 47, 7 + 11 + 43, 9 + 11 + 41, 7 + 13 + 41, 3 + 17 + 41, 7 + 17 + 37, 11 + 13 + 37, 5 + 19 + 37, 7 + 23 + 31, 11 + 19 + 31, 13 + 19 + 29 **Answer**

Question (11) Write five pairs of prime number less than 20 whose sum is divisible by 5.

**Answer** 2 and 3; 2 and 13; 3 and 17; 7 and 13, 11 and 19

Question (12) Fill in the blanks

(a) A number which has only two factors is called a _____.

**Answer**: A number which has only two factors is called a ** Prime Number**.

(b) A number which has more than two factors is called a ______.

**Answer**: A number which has more than two factors is called a ** Composite Number** .

(c) 1 is neither _____ nor ______.

**Answer**: 1 is neither ** Prime Number** nor

**.**

__Composite Number__(d) The smallest prime number is ______

**Answer**: The smallest prime number is ** two (2)**.

(e) The smallest composite number is ______

**Answer**: The smallest composite number is ** four (4)**.

(f) The smallest even number is ________

**Answer**: The smallest even number is ** two (2)**.