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co-prime numbers

A pair of numbers that does not have any common factors other than 1 are called
co-prime numbers.

example: Factors of 15 = 1, 3, 5 and 15
The only common factor is 1. Note
Factors of 16 = 1, 2, 4, 8 and 16 Any two

So, 15 and 16 are co-prime numbers. consecutive
numbers are always
twin Prime numbers co-prime numbers.

Pair of prime numbers that differ by 2 are called twin prime numbers. For example,
Š 3 and 5 are twin prime numbers.

Š 11 and 13 are twin prime numbers.

example: Check the following number is prime or composite.
(a) 43 (b) 56 (c) 91 (d) 97

Solution:
(a) Factors of 43 = 1 × 43

Clearly, 43 has two factors, 1 and the number itself. So, it is a prime number.

(b) 56 = 1 × 56 = 2 × 28 = 4 × 14 = 7 × 8

Factors of 56 = 1, 2, 4, 7, 8, 14, 28 and 56

Clearly, 56 has more than two factors, i.e., 8 factors. So, it is a composite number.

(c) 91 = 1 × 91 = 7 × 13

Factors of 91 = 1, 7, 13 and 91

Clearly, 91 has more than two factors, i.e., 4 factors. So, it is a composite number.
(d) 97 = 1 × 97

Factors of 97 = 1 and 97
Clearly, 97 has two factors, 1 and the number itself. So, it is a prime number.

Prime Factorisation

The process of expressing a number as a product of its prime factors only is called the
prime factorisation.
For example, 12 = 2 × 2 × 3, 18 = 2 × 3 × 3, 10 = 2 × 5, etc.

There are two methods of prime factorisation.

(a) Factor tree method (b) Division method

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