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: \[ \text{GCF} = 11 \]