To express the number 45 as a product of its prime factors, we can factor it step by step:
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Start by dividing 45 by the smallest prime number, which is 3: \[ 45 \div 3 = 15 \] So, we have 45 = 3 × 15.
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Next, factor 15 by dividing it by 3 again: \[ 15 \div 3 = 5 \] Thus, 15 = 3 × 5, and we can update our factorization: \[ 45 = 3 × 3 × 5. \]
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This can also be expressed using exponents: \[ 45 = 3^2 × 5^1. \]
So, the prime factorization of 45 is: \[ 45 = 3^2 \times 5. \]
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