Sure, I'd be happy to help you understand this problem step-by-step.
We need to factor out the greatest common factor (GCF) from the expression [tex]\(60m - 40\)[/tex].
1. Identify the GCF of 60 and 40:
- The GCF is the largest number that can evenly divide both 60 and 40.
- The factors of 60 are [tex]\(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60\)[/tex].
- The factors of 40 are [tex]\(1, 2, 4, 5, 8, 10, 20, 40\)[/tex].
- The highest common factor between 60 and 40 is 20.
Therefore, the GCF of 60 and 40 is [tex]\(20\)[/tex].
2. Factor out the GCF from each term in the expression [tex]\(60m - 40\)[/tex]:
- Divide [tex]\(60m\)[/tex] by the GCF [tex]\(20\)[/tex]:
[tex]\[
\frac{60m}{20} = 3m
\][/tex]
- Divide [tex]\(-40\)[/tex] by the GCF [tex]\(20\)[/tex]:
[tex]\[
\frac{-40}{20} = -2
\][/tex]
3. Rewrite the expression using the GCF and the simplified terms:
[tex]\[
60m - 40 = 20 \cdot (3m) - 20 \cdot (2)
\][/tex]
4. Combine the terms inside parentheses:
[tex]\[
60m - 40 = 20 \cdot (3m - 2)
\][/tex]
So, the factored form of the expression [tex]\(60m - 40\)[/tex] is:
[tex]\[
20 \cdot (3m - 2)
\][/tex]
Therefore, the answer is:
[tex]\[
\boxed{20 \cdot (3m - 2)}
\][/tex]
