To find the prime factorization of 1200, we start by dividing the number by the smallest prime numbers and continuing this process with the quotient until we reach 1.
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Start with 1200 and divide by 2 (the smallest prime): \[ 1200 \div 2 = 600 \] \[ 600 \div 2 = 300 \] \[ 300 \div 2 = 150 \] \[ 150 \div 2 = 75 \]
We have divided by 2 a total of 4 times.
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Next, we divide 75 by the next smallest prime number, which is 3: \[ 75 \div 3 = 25 \]
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Finally, we divide 25 by 5: \[ 25 \div 5 = 5 \] \[ 5 \div 5 = 1 \]
We have divided by 5 a total of 2 times.
Now, combining all the factors, we have:
- 2 used 4 times
- 3 used 1 time
- 5 used 2 times
Thus, we can express the prime factorization of 1200 as: \[ 1200 = 2^4 \times 3^1 \times 5^2 \] This is the prime factorization of 1200 in exponential form.
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