Pritchard Barber
10/13/2023 · Elementary School
Find the prime factorization of 345.
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Step-by-step Solution
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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