NCERT Solutions for Class 6 Maths Chapter 3 - Playing With Numbers Exercise 3.2

Exercise 3.2

1. What is the sum of any two:

a) Odd numbers.

Ans: 

Let us take an example \[1+3=4\]. Thus, we can say that the sum of any two 

odd numbers is an even number.

b) Even numbers.

Ans: 

Let us take an example \[2+4=6\]. Thus, we can say that the sum of any two 

even numbers is an even number.

2. State whether the following statements are true or false:

a) The sum of three odd numbers is even.

Ans: 

Let us check by taking an example: \[1+3+5=9\]. So, the given statement is 

false.

b) The sum of two odd numbers and one even number is even.

Ans:

Let us check by taking an example: \[1+3+2=6\]. So, the given statement is 

true.

c) The product of three odd numbers is odd.

Ans:

Let us check by taking an example: \[1\times 3\times 5=15\]. So, the given 

statement is true.

d) If an even number is divided by \[\mathrm{2}\], the quotient is always odd.

Ans:

Let us check by taking an example: \[\frac{4}{2}=2\]. So, the given statement 

is false.

e) All prime numbers are odd.

Ans:

\[\text{2}\] is prime and even. So the given statement is false.

f) Prime numbers do not have any factors.

Ans:

\[2\times 1=2\], here \[2\] is prime and having \[1,2\] but having \[2,1\] as 

factors. So, the given statement is false.

g) The Sum of two prime numbers is always even.

Ans:

Let us check by taking an example: \[2+6=8\]. So, the given statement is true.

h) \[\mathrm{2}\] is the only even prime number.

Ans:

The given statement is true.

i) All even numbers are composite numbers.

Ans:

Given statement is false because \[\text{2}\] is an even prime number.

j) The product of two even numbers is always even. 

Ans:

Let us check by taking an example: \[2\times 6=12\]. So, the given statement 

is true.

k)  The numbers \[\mathrm{13}\] and \[\mathrm{31}\] are primenumbers.Both these numbers have the same digits \[\mathrm{1}\] and \[\mathrm{3}\]. Find such pairs of prime numbers up to \[\mathrm{100}\].

Ans: \[\text{17}\] and \[\text{71}\]; \[37\] and \[73\]; \[79\] and \[97\].

3. The numbers 13 and 31 are prime numbers. Both these numbers have the same digits 1 and 3. Find such pairs of prime numbers up to 100.

Ans:

The following are the prime numbers up to 100 that have the same digits:

17 and 71

37 and 73

79 and 97

4. Write down separately the prime and composite numbers less than \[\mathrm{20}\].

Ans:

Prime numbers less than \[\text{20}\] are \[\text{2,3,5,7,11,13,17,19}\].

Composite numbers less than \[\text{20}\] are \[\text{4,6,8,9,10,12,14,15,16,18}\].

5. What is the greatest prime number between \[\mathrm{1}\] and \[\mathrm{10}\]?

Ans: The greatest prime number below \[\text{10}\] is \[\text{7}\].

6. Express the following as the sum of two odd numbers:

a) \[\mathrm{44}\]

Ans: 

We can write \[\text{44}\] as \[\text{3+41}\] which is the sum of two odd 

numbers.

b) \[\mathrm{36}\]

Ans:

We can write \[36\] as \[\text{3+33}\] which is the sum of two odd numbers.

c) \[\mathrm{24}\]

Ans:

We can write \[24\] as \[\text{1+23}\] which is the sum of two odd numbers.

d) \[\mathrm{18}\]

Ans:

We can write \[18\] as \[\text{1+17}\] which is the sum of two odd numbers.

7. Give three pairs of prime numbers whose difference is \[\mathrm{2}\]. (Remark: Two prime numbers whose difference is \[\mathrm{2}\] are called twin primes.)

Ans:

\[\text{1,3}\],\[\text{3,5}\] and \[\text{5,7}\] are twin primes because their respective differences are \[\text{2}\].

8. Which of the following numbers are prime:

a) \[\mathrm{23}\]

Ans:

\[\text{23}\] is a prime number because it has no factors rather than 

\[\text{1,23}\].

b) \[\mathrm{51}\]

Ans:

\[51\] is a prime number because it has no factors rather than \[\text{1,51}\].

c) \[\mathrm{37}\]

Ans:

\[37\] is a prime number because it has no factors rather than \[\text{1,37}\].

d) \[\mathrm{26}\]

Ans:

\[26\] is not a prime number because it has factors more than \[\text{1,26}\].

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

Ans:

\[90,91,92,93,94,95,96\] are the only seven consecutive numbers less than \[100\].

10. Express each of the following numbers as the sum of three odd primes:

a) \[\mathrm{21}\]

Ans: 

\[\text{17+3+1}\] is the sum for \[\text{21}\] expressed in sum of \[\text{3}\] 

odd numbers.

b) \[\mathrm{31}\]

Ans: 

\[\text{27+3+1}\] is the sum for \[31\] expressed in sum of \[\text{3}\] odd 

numbers.

c) \[\mathrm{53}\]

Ans: 

\[\text{49+3+1}\] is the sum for \[53\] expressed in sum of \[\text{3}\] odd 

numbers.

d) \[\mathrm{61}\]

Ans: 

\[\text{57+3+1}\] is the sum for \[61\] expressed in sum of \[\text{3}\] odd 

numbers.

11. Write five pairs of prime numbers less than \[\mathrm{20}\] whose sum is divisible by \[\mathrm{5}\].

Ans:

\[\text{3+7=10}\],\[7+13=20\],\[2+3=5\],\[3+17=20\] and \[5+5=10\].

Thus, \[3,7\]; \[7,13\]; \[2,3\]; \[3,17\]; \[5,5\] are the five pairs of numbers less than \[20\] whose sum is divisible by \[5\].

12. Fill in the blanks:

a) A number that has only two factors is called a ………..

Ans: Prime number.

b) A number that has more than two factors is called a ……….

Ans: Composite number.

c) \[\mathrm{1}\] neither ………. nor …………….

Ans: Prime nor a composite number.

d) The smallest prime number is …………….

Ans: \[\text{2}\] is the smallest prime number.

e) The smallest composite number is …………...

Ans: \[4\] is the smallest composite number.

f) The smallest even number is …………...

Ans: \[2\] is the smallest even number.

Conclusion

In conclusion, Ex 3.2 Class 6 Maths NCERT Solutions has provided a solid understanding of prime and composite numbers. We have learned how to identify these numbers and recognize their unique properties. Understanding these concepts is crucial for building a strong foundation in mathematics, as they play a key role in various mathematical operations and problem-solving techniques. By completing class 6 maths ex 3.2, students will be well-prepared to tackle more complex mathematical challenges with confidence. Keep practising to enhance your number skills and deepen your understanding of prime and composite numbers.

Class 6 Maths Chapter 3: Exercises Breakdown

CBSE Class 6 Maths Chapter 3 Other Study Materials

Chapter-Specific NCERT Solutions for Class 6 Maths

Given below are the chapter-wise NCERT Solutions for Class 6 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.