Question

1. what is the gcf of 12, 56, and 40?

Explanation:

Step1: Find factors of 12

The factors of 12 are all the numbers that divide 12 without leaving a remainder. So, \(12\div1 = 12\), \(12\div2 = 6\), \(12\div3 = 4\), \(12\div4 = 3\), \(12\div6 = 2\), \(12\div12 = 1\). Thus, the factors of 12 are \(1, 2, 3, 4, 6, 12\).

Step2: Find factors of 56

For 56, we have \(56\div1 = 56\), \(56\div2 = 28\), \(56\div4 = 14\), \(56\div7 = 8\), \(56\div8 = 7\), \(56\div14 = 4\), \(56\div28 = 2\), \(56\div56 = 1\). So the factors of 56 are \(1, 2, 4, 7, 8, 14, 28, 56\).

Step3: Find factors of 40

For 40, \(40\div1 = 40\), \(40\div2 = 20\), \(40\div4 = 10\), \(40\div5 = 8\), \(40\div8 = 5\), \(40\div10 = 4\), \(40\div20 = 2\), \(40\div40 = 1\). So the factors of 40 are \(1, 2, 4, 5, 8, 10, 20, 40\).

Step4: Identify common factors

Now, we find the common factors among 12, 56, and 40. Looking at the factor lists:

• Common factors from 12's factors (\(1, 2, 3, 4, 6, 12\)) and 56's factors (\(1, 2, 4, 7, 8, 14, 28, 56\)) are \(1, 2, 4\).
• Then, checking these against 40's factors (\(1, 2, 4, 5, 8, 10, 20, 40\)), the common factors are still \(1, 2, 4\).

Step5: Determine the GCF

The greatest common factor (GCF) is the largest number among the common factors. Among \(1, 2, 4\), the largest is 4.

Answer:

The GCF of 12, 56, and 40 is 4.