King Ward
05/30/2024 · High School
What is the greatest common factor (GCF) of 12 and 18?
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Step-by-step Solution
To find the greatest common factor (GCF) of 12 and 18, we can start by determining the prime factorization of each number.
- The prime factorization of 12 is:
\[
12 = 2^2 \times 3^1
\]
- The prime factorization of 18 is:
\[
18 = 2^1 \times 3^2
\]
Next, we identify the common prime factors and take the lowest power of each common factor:
- For the prime factor 2, the lowest power in the factorizations is \(2^1\).
- For the prime factor 3, the lowest power in the factorizations is \(3^1\).
Now, we multiply these together to find the GCF:
\[
\text{GCF} = 2^1 \times 3^1 = 2 \times 3 = 6
\]
Thus, the greatest common factor of 12 and 18 is \(\boxed{6}\).
Quick Answer
The GCF of 12 and 18 is 6.
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