Question

What is the greatest common factor of 33 and 22?

Answer 1

To find the greatest common factor (GCF) of 33 and 22, we can start by determining the prime factorizations of both numbers.

**Step 1: Factor 33**
- The prime factorization of 33 is:
\[
33 = 3 \times 11
\]

**Step 2: Factor 22**
- The prime factorization of 22 is:
\[
22 = 2 \times 11
\]

**Step 3: Identify the common factors**
- The common prime factors in both factorizations are:
- From 33: \(3\), \(11\)
- From 22: \(2\), \(11\)

The only common factor is \(11\).

**Step 4: State the GCF**
Thus, the greatest common factor of 33 and 22 is:
\[
\text{GCF} = 11
\]