Prime Factorization of 68

Find the prime factorization of 68. Express 68 as a product of prime numbers.

Prime factorization of
Answer: 68 = 2^2 × 17
Step-by-Step Solution
Step 1 Understand Prime Factorization

To find the prime factorization of 68, we need to express it as a product of prime numbers.


We do this by repeatedly dividing by the smallest prime that divides evenly, starting with 2.

A prime number is only divisible by 1 and itself (2, 3, 5, 7, 11, 13, ...).

Step 2 Divide by 2

Since 68 is even, we start by dividing by 2. We can divide by 2 twice:


68 ÷ 2 = 34
34 ÷ 2 = 17

After dividing by 2, we have 17 remaining.

Step 3 Final Prime Factor

We are left with 17, which is greater than 1.

17 cannot be divided by any prime smaller than its square root.

Therefore, 17 is itself a prime number and is our final factor.

Step 4 Write the Prime Factorization

Now we combine all the prime factors we found:


Expanded form: 68 = 2 × 2 × 17


Exponential form: 68 = 2^2 × 17


We can verify: 2 × 2 × 17 = 68 ✓