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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 ______.

(a) prime number (b) Composite number (c) Prime number, Composite number (d) 2 (e) 4 (f) 2

11. Write five pairs of prime numbers less than 20 whose sum is divisible by 5. (Hint : 3+7 = 10)

Five pairs of prime numbers less than 20 whose sum is divisible by 5 are : 2+3=5 2+13=15 3+17=20 7+13=20 19+11=30

10. Express each of the following numbers as the sum of three odd primes:
(a) 21          (b) 31          (c) 53          (d) 61

(a) 21 = 3 + 7 + 11 (b) 31 = 5 + 7 + 19 (c) 53 = 3 + 19 + 31 (d) 61 = 11 + 19 + 31

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

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

8. Which of the following numbers are prime?
(a) 23     (b) 51     (c) 37      (d) 26

(a) 23,23=1 23,23=23 123,23=1 23,23=23 1 23 has only two factors, 1 and 23. Therefore, it is a prime number. (b) 51,51=1 51,51=3 1751,51=1 51,51=3 17 51 has four factors, 1, 3, 17, 51. Therefore, it is not a prime number. It is a composite number. (c) 37 It has only two factors, 1 and 37. Therefore, it is a prime number. (d) 26 26 has four factors (1, 2, 13, 26). Therefore, it is not a...

7. Give three pairs of prime numbers whose difference is 2.
[Remark: Two prime numbers whose difference is 2 are called twin primes].

three pairs of prime numbers whose difference is 2 are : 3,5 41,43 and 71,73

6. Express the following as the sum of two odd primes.
(a) 44     (b) 36      (c) 24        (d) 18

(a) 44 = 37 +7 (b) 36 = 31 +5 (c) 24 = 19 +5 (d) 18 = 11 +7

5. What is the greatest prime number between 1 and 10?

Prime numbers between 1 and 10 are 2, 3, 5, and 7. Among these numbers, 7 is the greatest.

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

Prime numbers less than 20 are : 2, 3, 5, 7, 11, 13, 17, 19 Composite numbers less than 20 are : 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

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.

Prime Number having the same digit are: 17,71 37,73 and  79,97

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.

(a) False, Because the sum of two odd number is even and the sum of even number and an odd number is odd, so the sum of three odd numbers is odd.      for example :      3 + 5 + 7 = 15, i.e., odd (b) True, as the sum of two odd number is even a sum of two even number is even.       for example :       3 + 5 + 6 = 14, i.e., even (c) True because the product of two odd number is odd and product...

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

(a) the sum of any two Odd numbers is always even. for e.g. 3 + 5 = 8 and 9 + 7 = 16 (b) the sum of any two Even numbers is always even. for e.g. 2 + 4 = 6 and 8 + 4 = 12
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