Question

What is the greatest common factor of 72, 60, and 56?

Answer 1

To find the greatest common factor (GCF) of the numbers 72, 60, and 56, we can start by finding the prime factorization of each number.

1. **Factorization of 72**:
\[
72 = 2^3 \times 3^2
\]

2. **Factorization of 60**:
\[
60 = 2^2 \times 3^1 \times 5^1
\]

3. **Factorization of 56**:
\[
56 = 2^3 \times 7^1
\]

Next, we identify the common prime factors from the factorizations of these numbers:

- The only prime factor common to all three numbers is \(2\).

Now, we determine the lowest power of the common prime factor:
- For \(2\):
- In 72, the power is \(3\) (i.e., \(2^3\)).
- In 60, the power is \(2\) (i.e., \(2^2\)).
- In 56, the power is \(3\) (i.e., \(2^3\)).

The minimum power of \(2\) present in all factorizations is \(2^2\).

Thus, the GCF can be calculated as:
\[
GCF = 2^2 = 4
\]

Therefore, the greatest common factor of 72, 60, and 56 is \(\boxed{4}\).