# prime factor of 42

#### Understand the Problem

The question is asking for the prime factors of the number 42, which involves identifying the prime numbers that multiply together to give 42.

2, 3, 7

The prime factors of 42 are 2, 3, and 7

#### Steps to Solve

1. Identify the smallest prime number that divides 42

Start with the smallest prime number which is 2. Divide 42 by 2. Since 42 is even, it is divisible by 2.

$$42 \div 2 = 21$$

1. Identify the next prime factor of 21

Next, look for the smallest prime number that can divide 21. The number 21 is not divisible by 2 (since it is odd), but it is divisible by 3 (since the sum of its digits, 2 + 1 = 3, is divisible by 3).

$$21 \div 3 = 7$$

1. Check if 7 is a prime

Lastly, we need to check if 7 is a prime number. Since 7 is only divisible by 1 and itself, it is a prime number. Thus, 7 is the last prime factor of 42.

1. Combine the prime factors

Multiplying all the prime factors together, we get:

$$2 \times 3 \times 7 = 42$$

Hence, the prime factors of 42 are 2, 3, and 7.

The prime factors of 42 are 2, 3, and 7