What is the prime factor of 68?

Understand the Problem

The question is asking for the prime factors of the number 68. To solve this, we need to find the prime numbers that, when multiplied together, give the product of 68.

The prime factors of 68 are $2$ and $17$.

The prime factors of 68 are $2$ and $17$.

Steps to Solve

1. Divide by the smallest prime number

Start with the smallest prime number, which is 2. Check if 68 is divisible by 2.

$$68 \div 2 = 34$$

Since the result is a whole number, 2 is a prime factor of 68.

1. Continue factoring

Next, take the quotient obtained and check if it's divisible by 2 again.

$$34 \div 2 = 17$$

So, 2 is also a prime factor again.

1. Check if the remaining number is prime

Now, we have 17, which we need to check if it is a prime number. The only divisors of 17 are 1 and 17 itself, indicating that it is a prime number.

1. List all prime factors

At this point, we have ( 68 = 2 \times 2 \times 17 ). The prime factors can be represented as:

$$2^2 \times 17$$

Thus, the prime factors of 68 are 2 and 17.

The prime factors of 68 are $2$ and $17$.