What is the prime factorization of 36 using exponents?

The prime factorization of 36 is expressed as 2² × 3².

To find this, we start by finding the prime factors of 36. We can do this by dividing 36 by the smallest prime number, which is 2:

• 36 ÷ 2 = 18

We can continue factoring 18 by dividing it by 2 again:

• 18 ÷ 2 = 9

Now, we have 9, which is not divisible by 2. Instead, we divide it by the next smallest prime number, which is 3:

• 9 ÷ 3 = 3

Finally, we divide 3 by itself:

• 3 ÷ 3 = 1

Now that we have reached 1, we can summarize our factors. We divided by 2 twice and by 3 twice:

• 2 × 2 × 3 × 3 = 36

We can express this in exponent form, resulting in the prime factorization of 36 as 2² × 3².