What is the prime factorization of 180?

The prime factorization of a number expresses that number as the product of its prime factors. To find the prime factorization of 180, we can start by dividing the number by the smallest prime number and continue dividing until we reach 1, using only prime numbers during this process.

1. Start with 180. Since it is even, we divide by 2:

• ( 180 ÷ 2 = 90 )

2. Repeat the process with 90, which is also even:

• ( 90 ÷ 2 = 45 )

3. Next, divide 45 by the smallest prime number that fits, which is 3:

• ( 45 ÷ 3 = 15 )

4. Continue with 15, again using 3:

• ( 15 ÷ 3 = 5 )

Now we have reached 5, which is a prime number. By gathering all the prime factors used in the divisions, we find:

• 2 appears twice (from the divisions by 2)

• 3 appears twice (from the divisions by 3)

• 5 appears once.

All together, this can be expressed as ( 2^2 ×