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.
-
Factorization of 72: \[ 72 = 2^3 \times 3^2 \]
-
Factorization of 60: \[ 60 = 2^2 \times 3^1 \times 5^1 \]
-
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 \(\boxed{4}\).