What is the prime factorization of 108 using exponents?

To find the prime factorization of 108, we start by dividing the number by the smallest prime number, which is 2.

108 is even, so we can divide it by 2:

• 108 ÷ 2 = 54

Now, we take 54 and continue dividing by 2:

• 54 ÷ 2 = 27

At this point, 27 is not divisible by 2, so we move to the next prime number, which is 3:

• 27 ÷ 3 = 9
• 9 ÷ 3 = 3
• 3 ÷ 3 = 1

Now that we’ve reached 1, we can summarize our divisions. The prime factors we used are 2 and 3. We counted how many times each prime factor was used:

• 2 appears twice (2 × 2)
• 3 appears three times (3 × 3 × 3)

So, the prime factorization of 108, using exponents, can be written as:

2² × 3³