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\\January 6, 2024 3:29 PM Bharat Arora Proof-3 Reader _________________________ Date: ___________________74

Example 4: Identify whether the following numbers are prime numbers or composite
numbers.

(a) 13 (b) 27 (c) 39 (d) 79
Solution: (a) Factors of 13 are 1 and 13; there are only two factors 1 and 13. So,
it is a prime number.

(b) Factors of 27 are 1, 3, 9 and 27; there are more Remember
than two factors. So, it is a composite number.  There are infinitely
many prime numbers.
(c) Factors of 39 are 1, 3, 13 and 39; there are more  2 is the smallest
than two factors. So, it is a composite number. and only even prime
number.
(d) Factors of 79 are 1 and 79; there are only two  3 is the smallest odd

factors 1 and 79. So, it is a prime number. prime number.

Think and Answer
1. List all the prime numbers less than 25. 2. List all the composite numbers less than 30.

Factorisation

Writing a number as a product of its factors (two or more) is called a factorisation.

For example, factorisation of 12 are 12 = 4 × 3 or 2 × 2 × 3 or 2 × 6

Prime Factorisation

Prime factorisation is the process of expressing a number as a product of its prime
factors or numbers.

Example 1: Find the prime factorisation of 24.
Solution: Follow the given steps to find the prime factors.

Step 1: Write the number as a product of a pair of factors. 24 = 2 × 12
Step 2: Among factors check for composite factors. In this case, it is 12.

Step 3: Factorise the composite factors as a product of its prime factors.
24 = 2 × 3 × 4 = 2 × 3 × 2 × 2
Step 4: Write all factors in an increasing order. 24 = 2 × 2 × 2 × 3

Thus, prime factorisation of 24 = 2 × 2 × 2 × 3.

We can also find prime factorisation using the factor tree method or division method.

Knowledge Desk
Fundamental property of prime factorisation: Every composite number can be expressed as
a product of its prime factors uniquely. In the prime factorisation of any number, the order
of factors does not matter. For example, 30 = 2 × 5 × 3 or 2 × 3 × 5

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