Asked by Maria Candea
Identify the greatest common factor of 66 and 48, z48z.
Answers
Answered by
GPT-4o mini
To find the greatest common factor (GCF) of 66 and 48, we can start by determining the prime factorization of each number.
1. **Prime factorization of 66**:
- The prime factors of 66 are \(2 \times 3 \times 11\).
2. **Prime factorization of 48**:
- The prime factors of 48 are \(2^4 \times 3\).
Now, we identify the common prime factors from both factorizations:
- From 66, the prime factors are \(2^1\), \(3^1\), and \(11^1\).
- From 48, the prime factors are \(2^4\) and \(3^1\).
The common factors are \(2\) and \(3\).
Now, we take the lowest exponent for each of the common prime factors:
- For \(2\), the lowest exponent is \(1\) (from 66).
- For \(3\), the lowest exponent is \(1\) (from both).
Now, we multiply these together to find the GCF:
\[
GCF = 2^1 \times 3^1 = 2 \times 3 = 6
\]
So, the greatest common factor of 66 and 48 is \(\boxed{6}\).
1. **Prime factorization of 66**:
- The prime factors of 66 are \(2 \times 3 \times 11\).
2. **Prime factorization of 48**:
- The prime factors of 48 are \(2^4 \times 3\).
Now, we identify the common prime factors from both factorizations:
- From 66, the prime factors are \(2^1\), \(3^1\), and \(11^1\).
- From 48, the prime factors are \(2^4\) and \(3^1\).
The common factors are \(2\) and \(3\).
Now, we take the lowest exponent for each of the common prime factors:
- For \(2\), the lowest exponent is \(1\) (from 66).
- For \(3\), the lowest exponent is \(1\) (from both).
Now, we multiply these together to find the GCF:
\[
GCF = 2^1 \times 3^1 = 2 \times 3 = 6
\]
So, the greatest common factor of 66 and 48 is \(\boxed{6}\).
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