Question

What is the prime factorization of 360?

Answer 1

To find the prime factorization of 360, we can begin by dividing the number by the smallest prime numbers.

1. Divide by 2 (the smallest prime):
\[
360 \div 2 = 180
\]

2. Divide by 2 again:
\[
180 \div 2 = 90
\]

3. Divide by 2 once more:
\[
90 \div 2 = 45
\]

4. Now, 45 is not divisible by 2, so we move to the next prime, which is 3:
\[
45 \div 3 = 15
\]

5. Divide by 3 again:
\[
15 \div 3 = 5
\]

6. Finally, 5 is a prime number.

Putting all this together, the prime factorization of 360 can be written as:
\[
360 = 2^3 \times 3^2 \times 5^1
\]

Thus, the complete prime factorization of 360 is:
\[
2^3 \times 3^2 \times 5
\]