Question

Express the prime factorization of 1,200 as a product of prime numbers with exponents.(2 points)
4 ⋅ 

Answer 1

To express the prime factorization of 1,200, we can start by dividing it by the smallest prime numbers until we reach 1.

1. Divide by 2:
- 1200 ÷ 2 = 600
- 600 ÷ 2 = 300
- 300 ÷ 2 = 150
- 150 ÷ 2 = 75

2. At this point, 75 can no longer be divided by 2, so we move to the next prime, which is 3:
- 75 ÷ 3 = 25

3. Now, we move to the next prime number, which is 5:
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1

Now we can count how many times each prime was used:
- 2 appears 4 times
- 3 appears 1 time
- 5 appears 2 times

Thus, the prime factorization of 1,200 is:
\[
1200 = 2^4 \cdot 3^1 \cdot 5^2
\]