2² x 3²
Step-by-step explanation: To find the prime factorization of 36, let's first begin by creating a factor tree with two branches. Since 36 ÷ 2 = 18, 2 and 18 are factors of 36. This means that we can write 2 and 18 at the bottom of our branches.
Next, we will circle and numbers that are prime in our factor tree. Since 2 is a prime number, we will circle it but 18 is not prime, so we will draw two more branches coming down from 18. Since 18 ÷ 2 = 9, 2 and 9 are factors of 18. Next, we will circle the two because it's prime but draw two more branches from 9 because it's composite
Since 9 ÷ 3 = 3, 3 and 3 are factors of 9, we will write 3 at the bottom of the branches. Since 3 and 3 are prime, we will circle them. Now that we have circle at the bottom of our branches, we are done. Therefore, the prime factorization of 36 is
2 × 2 × 3 × 3. Notice that 2 is repeated two times and 3 is repeated two times so we can rewrite the prime factorization using exponents.
Therefore, the prime factorization would be 2² × 3².
