Question

What is the greatest common factor of 66, 44, and 22?

Answer 1

To find the greatest common factor (GCF) of the numbers 66, 44, and 22, we can first determine the prime factorization of each number.

1. **Prime Factorization**:
- For **66**:
\[
66 = 2 \times 3 \times 11
\]
- For **44**:
\[
44 = 2^2 \times 11
\]
- For **22**:
\[
22 = 2 \times 11
\]

2. **Identify Common Prime Factors**:
The common prime factors of all three numbers are:
- \(2\)
- \(11\)

3. **Determine the Lowest Powers**:
- The lowest power of \(2\) in the factorizations is \(2^1\).
- The lowest power of \(11\) is \(11^1\).

4. **Calculate the GCF**:
The GCF is the product of the common prime factors raised to the lowest powers:
\[
\text{GCF} = 2^1 \times 11^1 = 2 \times 11 = 22
\]

Therefore, the greatest common factor of 66, 44, and 22 is \( \boxed{22} \).