# Greatest Common Factor of 2 Numbers

To find the **greatest common factor **(gcf) of two given numbers,

- First we list all the factors of the two numbers.
- Then, we look for the common factors of these numbers.
- We find the greatest number among these common factors which will be the greatest common factor (gcf) of the two given numbers.

Find the greatest common factor of 16 and 24.

### Solution

**Step 1:**

The factors of 16 and 24 are

16 = **1, 2, 4, 8**, 16

24 = **1, 2**, 3, **4**, 6, **8**, 12, 24

**Step 2:**

The common factors of 16 and 24 are shown in bold.

**Step 3:**

The greatest among these is 8. So the greatest common factor (gcf) of 16 and 24 is 8.

Find the greatest common factor of 84 and 108.

### Solution

**Step 1:**

The factors of 84 and 108 are

84 = **1, 2, 3, 4, 6**, 7, **12**, 14, 21, 28, 42, 84

108 = **1, 2, 3, 4, 6**, 9, **12**, 18, 27, 36, 54, 108

**Step 2:**

The common factors of 84 and 108 are shown in bold.

**Step 3:**

The greatest among these is 12. So the greatest common factor (gcf) of 84 and 108 is 12.

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