The prime factorization of 288 is 25 × 32.
To arrive at this result, we start by dividing 288 by the smallest prime number, which is 2:
- 288 ÷ 2 = 144
- 144 ÷ 2 = 72
- 72 ÷ 2 = 36
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
At this point, we cannot divide by 2 anymore since 9 is not even. So we move to the next prime, which is 3:
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
Now that we have reached 1, we can collect our prime factors. From our divisions, we see that:
- We divided by 2 a total of 5 times.
- We divided by 3 a total of 2 times.
So, we can express 288 as the product of these prime factors: 25 × 32.