What is the greatest common factor of 8m, 36m³, and 12?

To find the greatest common factor (GCF) of the numbers 8m, 36m³, and 12, we need to look at the coefficients and the variable parts separately.

First, we find the GCF of the numerical coefficients: 8, 36, and 12.

• The factors of 8 are: 1, 2, 4, 8.
• The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.
• The factors of 12 are: 1, 2, 3, 4, 6, 12.

The common factors of 8, 36, and 12 are: 1, 2, 4.

The greatest of these is 4.

Now, we consider the variable parts. The term 8m has one ‘m’, and 36m³ has three ‘m’s, while 12 has no ‘m’ at all. Since 12 doesn’t contain ‘m’, we take the lowest power of ‘m’ that appears in any of the terms, which is ‘m⁰‘ or just 1.

Combining both the GCF of the coefficients and the variable part, we have:

GCF = 4 * 1 = 4.

Thus, the GCF of 8m, 36m³, and 12 is 4.