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\\October 8, 2025 12:13 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74
co-prime numbers
A pair of numbers that do not have any common factors other than 1 is a pair of co-prime
numbers.
example: Factors of 15 = 1, 3, 5 and 15
The only common factor is 1.
Factors of 16 = 1, 2, 4, 8 and 16
So, 15 and 16 are co-prime numbers. Be Aware
twin Prime numbers Any two consecutive numbers are
always co-prime numbers.
Pairs of prime numbers that differ by 2 are called twin prime numbers. For example:
3 and 5 are twin prime numbers.
11 and 13 are twin prime numbers.
example: Check whether the following numbers are prime or composite.
( a) 43 (b) 56 (c) 91 (d) 97
Solution:
( a) 43 = 1 × 43
Factors of 43 = 1 and 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 is called 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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