September 15, 2024

# What is the HCF of smallest prime number and the smallest composite number?

 Prime numbers:    A  number having exactly two different factors , namely 1 and itself is called a prime number. Clearly , 1 has only one factor , namely 1 itself. $\therefore$ 1 is neither prime nor composite. Examples : The first 25 prime numbers (all the prime numbers less than 100) are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 Note:  The smallest prime number is 2 and it is the only even prime number. Composite numbers:  A number having more than two different factors is called composite number. Examples :  4, 6, 8 ,10 , 15, 20, 27  all are composite numbers. Note : The smallest composite number is 4.

## Que . What is the HCF of smallest prime number and the smallest composite number?

Solution : Since the smallest prime number is 2 and  the smallest composite number is 4, we have to find  the HCF of  2 and 4.

To find the HCF of 2 and 4 let us write their prime factorization.

2 = 2

4 = 2 × 2

HCF (2, 4) = 2

Thus, the HCF of the smallest composite number and the smallest prime number is 2.

Answer: Thus, the HCF of the smallest composite number and the smallest prime number is 2.

#### Bina singh

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