Pritchard Barber
10/13/2023 · Elementary School

Find the prime factorization of 345.

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To find the prime factorization of 345, we can start by dividing it by the smallest prime numbers. 1. **Check divisibility by 2**: 345 is odd, so it is not divisible by 2. 2. **Check divisibility by 3**: The sum of the digits of 345 is \(3 + 4 + 5 = 12\), which is divisible by 3. Therefore, 345 is divisible by 3. \[ 345 \div 3 = 115 \] 3. **Now factor 115**: Check divisibility by 3 again. The sum of the digits of 115 is \(1 + 1 + 5 = 7\), which is not divisible by 3. 4. **Check divisibility by 5**: The last digit of 115 is 5, so it is divisible by 5. \[ 115 \div 5 = 23 \] 5. **Now factor 23**: The number 23 is a prime number. Putting it all together, we have: \[ 345 = 3 \times 5 \times 23 \] Thus, the prime factorization of 345 is: \[ \boxed{3 \times 5 \times 23} \]

Quick Answer

The prime factorization of 345 is \(3 \times 5 \times 23\).
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