What is the prime factorization of 432?

The prime factorization of 432 is 2⁴ × 3³.

To find the prime factorization, we start by dividing 432 by the smallest prime number, which is 2. Since 432 is even, we can continue dividing by 2 until we can no longer do so:

• 432 ÷ 2 = 216
• 216 ÷ 2 = 108
• 108 ÷ 2 = 54
• 54 ÷ 2 = 27

Now, 27 is not divisible by 2, so we move to the next prime number, which is 3:

• 27 ÷ 3 = 9
• 9 ÷ 3 = 3
• 3 ÷ 3 = 1

At this point, we’ve reached 1, and we can summarize the divisions we performed:

We divided by 2 a total of 4 times (2⁴) and by 3 a total of 3 times (3³). Therefore, the complete prime factorization of 432 is:

2⁴ × 3³