Page 146 - Ganit Kaushal

7. 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 ________ .
8. 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.
9. Which of the following numbers are prime?

(a) 29 (b) 57 (c) 43 (d) 61
10. Which of the following pairs of numbers are co-prime?
(a) 12 and 35 (b) 15 and 37 (c) 27 and 32 (d) 17 and 85

(e) 515 and 516 (f) 215 and 415
11. Express each of the following numbers as the sum of two odd primes.
(a) 24 (b) 36 (c) 84 (d) 98

12. Express each of the following numbers as the sum of twin primes.
(a) 24 (b) 36 (c) 84 (d) 120
13. Express each of the following numbers as the sum of three odd primes.

(a) 21 (b) 35 (c) 49 (d) 63
14. Write five pairs of prime numbers less than 20 whose sum is divisible by 5.

5.5 PRIME FACTORISATION

We have already learnt the method of factorisation in the previous sections. Factorisation of a number is a
method of expressing that number as the product of its factors. For example:

(i) 24 = 4 × 6, here 24 is factorised into its two factors, 4 and 6.
(ii) 24 = 2 × 12, here 24 is factorised into its two factors, 2 and 12.
(iii) 24 = 3 × 8, here 24 is factorised into its two factors, 3 and 8.

What is Prime Factorisation?
Prime factorisation of a number is the method of expressing that number as the product of its prime
factors. This is also known as complete factorisation.
How to find prime factorisation?

The following three methods are generally used to find prime factorisation:

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