Suppose you need to find the GCF of three or more numbers, and you’d really prefer to avoid prime factorizing. Is there a way? Sure there is … here’s how.

**Example: Find the GCF for 18, 42 and 96**

**Step 1)** Write the numbers down from left to right, like this:

………. 18 42 96

[FYI, the periods: …. are there just to indent the numbers. They have no mathematical meaning.]

**Step 2)** Find any number that goes into all three numbers. You don’t need to choose the largest such number. Suppose we use the number 2. Write that number to the left of the three numbers. Then divide all three numbers by 2 and write the results below the numbers like this:

**2** | 18 42 96

…….. 9 21 48

**Step 3)** Find another number that goes into all three remaining numbers. It could be the same number. If it is, use that. If not, use any other number that goes into the remaining numbers. In this example, 3 goes into all of them. So write down the 3 to the left and once again show the results of dividing, like this:

**2** | 18 42 96

**3** | 9 21 48

……… 3 7 16

**Step 4)** You’ll eventually reach a stage at which there’s no other number that goes into all of the remaining numbers. Once at that stage, just multiply the numbers in the far-left column, the numbers you pulled out. In this case, those are the numbers: **2** and **3**. Just multiply those numbers together, and that’s the **GCF**. So in this example, the **GCF is 2 x 3 = 6**, and that’s all there is to it.

Now try this yourself by doing these problems. Answers are below.

a) 18, 45, 108

b) 48, 80, 112

c) 32, 72, 112

d) 24, 60, 84, 132

e) 28, 42, 70, 126, 154

**Answers:**

a) GCF = 9

b) GCF = 16

c) GCF = 8

d) GCF = 12

e) GCF = 14

Comments on:"How to find the GCF of 3+ Numbers — FAST … no prime factorizing" (2)470 Greatest Common Factors of Pythagorean Triples. | Find the Factorssaid:[…] Mathchat has written an excellent post on finding the greatest common factor of three or more numbers that can be used for all integers in general. […]

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stellasaid:wow this tip is cool!!!!

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