To express the prime factorization of 1,200, we can start by dividing it by the smallest prime numbers until we reach 1.
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Divide by 2:
- 1200 ÷ 2 = 600
- 600 ÷ 2 = 300
- 300 ÷ 2 = 150
- 150 ÷ 2 = 75
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At this point, 75 can no longer be divided by 2, so we move to the next prime, which is 3:
- 75 ÷ 3 = 25
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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: \[ 1200 = 2^4 \cdot 3^1 \cdot 5^2 \]
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