What is the prime factorization of 180?

To find the prime factorization of 180, we can start by dividing it by the smallest prime number, which is 2. We keep dividing by 2 until we get an odd number:

180 ÷ 2 = 90 90 ÷ 2 = 45

Now 45 is an odd number, so we need to find its prime factors. We can try dividing it by the smallest prime number, which is 3:

45 ÷ 3 = 15

15 is still an odd number, so we need to find its prime factors:

15 ÷ 3 = 5

5 is a prime number. We have now found all the prime factors of 180. We can write them as a product of primes:

180 = 2 x 2 x 3 x 3 x 5

So the prime factorization of 180 is 2 x 2 x 3 x 3 x 5, or 2² x 3² x 5.