To find the prime factorization of 360, we can begin by dividing the number by the smallest prime numbers.
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Divide by 2 (the smallest prime): \[ 360 \div 2 = 180 \]
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Divide by 2 again: \[ 180 \div 2 = 90 \]
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Divide by 2 once more: \[ 90 \div 2 = 45 \]
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Now, 45 is not divisible by 2, so we move to the next prime, which is 3: \[ 45 \div 3 = 15 \]
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Divide by 3 again: \[ 15 \div 3 = 5 \]
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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: \[ 2^3 \times 3^2 \times 5 \]