Question

find the greatest common factor (gcf). 20 and 32

Explanation:

Step1: Find factors of 20

The factors of 20 are all the numbers that divide 20 without leaving a remainder. So, \(1, 2, 4, 5, 10, 20\) (since \(20\div1 = 20\), \(20\div2 = 10\), \(20\div4 = 5\), \(20\div5 = 4\), \(20\div10 = 2\), \(20\div20 = 1\)).

Step2: Find factors of 32

The factors of 32 are the numbers that divide 32 without a remainder. So, \(1, 2, 4, 8, 16, 32\) (since \(32\div1 = 32\), \(32\div2 = 16\), \(32\div4 = 8\), \(32\div8 = 4\), \(32\div16 = 2\), \(32\div32 = 1\)).

Step3: Identify common factors

Now, we look for the numbers that are in both lists of factors. The common factors of 20 and 32 are \(1, 2, 4\).

Step4: Determine the GCF

Among the common factors \(1, 2, 4\), the greatest one is 4.

Answer:

4