- Prime Numbers Factors and Multiples
- Home
- Even and Odd Numbers
- Divisibility Rules for 2, 5, and 10
- Divisibility Rules for 3 and 9
- Factors
- Prime Numbers
- Prime Factorization
- Greatest Common Factor of 2 Numbers
- Greatest Common Factor of 3 Numbers
- Introduction to Distributive Property
- Understanding the Distributive Property
- Introduction to Factoring With Numbers
- Factoring a Sum or Difference of Whole Numbers
- Least Common Multiple of 2 Numbers
- Least Common Multiple of 3 Numbers
- Word Problem Involving the Least Common Multiple of 2 Numbers

# Greatest Common Factor of 3 Numbers

Given three numbers, the method of finding greatest common factor is same as the method of finding gcf of two numbers.

- We list all the factors of the three numbers.
- We look for the common factors of these numbers.
- Among these we find for the greatest number which will be the gcf of the three given numbers.

Find the greatest common factor of 18, 24 and 36

### Solution

**Step 1:**

The factors of 18 and 24 and 36 are

18 = **1, 2, 3, 6**, 9, 18

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

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

**Step 2:**

The common factors of 18, 24 and 36 are shown in bold.

**Step 3:**

The greatest among these is 6. So the greatest common factor (gcf) of 18, 24 and 36 is 6.

Find the greatest common factor of 15, 35 and 75

### Solution

**Step 1:**

The factors of 15, 35 and 75 are

15 = **1**, 3, **5**, 15

35 = **1, 5**, 7, 35

75 = **1**, 3, **5**, 15, 25, 75

**Step 2:**

The common factors of 15, 35 and 75 are shown in bold.

**Step 3:**

The greatest among these is 5. So the greatest common factor (gcf) of 15, 35 and 75 is 5.

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