Skill: Find the greatest common factor

A factor is a whole number that divides another number evenly, with no remainder. To find the greatest common factor (GCF) of two numbers:

1. List the factors of each number.
2. Find the factors that appear in both lists.
3. Choose the largest shared factor.

Example: Find the GCF of $24$ and $36$.

First, list the factor pairs of $24$:

$$1 \times 24,\quad 2 \times 12,\quad 3 \times 8,\quad 4 \times 6$$

So, the factors of $24$ are:

$$1,\ 2,\ 3,\ 4,\ 6,\ 8,\ 12,\ 24$$

Now list the factor pairs of $36$:

$$1 \times 36,\quad 2 \times 18,\quad 3 \times 12,\quad 4 \times 9,\quad 6 \times 6$$

So, the factors of $36$ are:

$$1,\ 2,\ 3,\ 4,\ 6,\ 9,\ 12,\ 18,\ 36$$

The factors that both numbers share are:

$$1,\ 2,\ 3,\ 4,\ 6,\ 12$$

The largest shared factor is $12$. Therefore,

$$\boxed{\text{GCF}(24,36)=12}$$

You can check: $24 \div 12=2$ and $36 \div 12=3$, so $12$ divides both numbers evenly.