July 17, 2024

What is the hcf of smallest prime number and the smallest composite number?

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.

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