# Find the HCF of the Smallest Prime Number and the Smallest Composite Number.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The HCF of the smallest prime number and the smallest composite number is 2. Finding the highest common factor (HCF) of two numbers is a fundamental concept in mathematics. In this case, we have to find the HCF of the smallest prime number and the smallest composite number. The HCF represents the largest number that divides both given numbers without leaving any remainder.

## Smallest Prime Number

A prime number is a positive integer greater than 1 that has exactly two positive divisors: 1 and itself. In other words, a prime number cannot be divided evenly by any other number except 1 and itself. These numbers include familiar examples like 2, 3, 5, 7, 11, and so on, and continue infinitely. The smallest prime number is 2.

To determine if a number is prime, we can check if it has any divisors other than 1 and itself. If it does not have any divisors other than those two, then it is a prime number. For example, let’s consider the number 7. It can only be divided evenly by 1 and 7, which are its only divisors. Therefore, 7 is a prime number.

## Smallest Composite Number

A composite number is a positive integer greater than 1 that has more than two divisors. In other words, it can be divided evenly by numbers other than 1 and itself. These numbers are the opposite of prime numbers, which have only two divisors: 1 and itself. The smallest composite number is 4.

To determine if a number is composite, we can check if it has divisors other than 1 and itself. If it does, then it is a composite number. For example, let’s consider the number 12. It can be divided evenly by 1, 2, 3, 4, 6, and 12, which means it has divisors other than 1 and itself. Therefore, 12 is a composite number.

## HCF of Smallest Prime and Composite Number

Smallest prime number = 2

Smallest composite number = 4

To find their HCF, we need to determine the largest number that can divide both 2 and 4 without leaving a remainder. In this case, the HCF is 2 since it is the largest common divisor of both numbers.

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

Summary:

## Find the HCF of the Smallest Prime Number and the Smallest Composite Number.

2 is the HCF of the smallest prime number and composite number. This means that 2 is the greatest number that can divide both 2 and 4 without leaving the remainder.

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