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Numbers which have more than two factors are called composite numbers. Example 4: Identify whether the following numbers are prime numbers or composite
numbers.
Finding Prime Numbers or composite Numbers (a) 13 (b) 27 (c) 39 (d) 79

To find whether a number is a prime number or a composite number, we first check Solution: (a) Factors of 13 are 1 and 13; there are only two factors 1 and 13. So,
it is a prime number.
whether it is an even number or an odd number, as every even number other than (b) Factors of 27 are 1, 3, 9 and 27; there are more Math Insight

2 is a composite number. than two factors. So, it is a composite number.  There are infinitely
many prime numbers.
If a number is odd, divide it by prime numbers 3, 5, 7, 11, and so on using the (c) Factors of 39 are 1, 3, 13 and 39; there are more  2 is the smallest

divisibility rules. If the remainder is 0, it is a composite number. than two factors. So, it is a composite number. and only even prime
number.
Example 1: Is 39 a prime number? (d) Factors of 79 are 1 and 79; there are only two  3 is the smallest odd
prime number.
factors 1 and 79. So, it is a prime number.
Solution: 39 is not divisible by 2 because it is not an even number. But, 39 is

divisible by 3 because 3 + 9 = 12, which is divisible by 3. Think Tank

Thus, 39 is not a prime number, it is a composite number. 1. List all the prime numbers less than 25. 2. List all the composite numbers less than 30.

Example 2: Is 65 a prime number? FactorisatioN

Solution: 65 is not divisible by 2 because it does not end with an even digit. 65 is

not divisible by 3 because 6 + 5 = 11 is not divisible by 3. Writing a number as a product of its factors (two or more) is called a factorisation.
For example: Factorisations of 12 are 12 = 4 × 3 or 2 × 2 × 3 or 2 × 6
65 is divisible by 5 because it ends with 5.
Prime Factorisation
Thus, 65 is not a prime number, it is a composite number.
Prime factorisation is the process of expressing a number as a product of its prime
Example 3: Is 89 a prime or composite number? factors or numbers.

Solution: 89 is not an even number. So, it is not divisible by 2. Example 1: Find the prime factorisation of 24.

8 + 9 = 17, 17 is not divisible by 3. 7 89 12 Q Solution: Follow the given steps to find the prime factors.
7 Step 1: Write the number as a product of a pair of factors. 24 = 2 × 12
So, 89 is not divisible by 3. 19 Step 2: Among the factors check for composite factors. In this case, it is 12.

89 is also not divisible by 5. 14
5 R Step 3: Factorise the composite factors as a product of its prime factors.
On dividing 89 by 7, we get the remainder 5. 24 = 2 × 3 × 4 = 2 × 3 × 2 × 2

So, 89 is not divisible by 7. Step 4: Write all the factors in an increasing order. 24 = 2 × 2 × 2 × 3
Thus, prime factorisation of 24 = 2 × 2 × 2 × 3.
Further, on dividing 89 by 11, we get the remainder 1.
We can also find prime factorisation using the factor tree method or division method.
So, 89 is not divisible by 11. 11 89 8 Q

Further division is not required as the quotient 8 is less than 88 R Knowledge Desk
1
the divisor 11. 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
Thus, 89 is a prime number. of factors does not matter. For example, 30 = 2 × 5 × 3 or 2 × 3 × 5

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