## Greatest Common Factor

September 27, 2010 9:45 am From the Teacher, Grade 4, Homeschoolers No More, Mathematics, Reviewers**Greatest Common factor or GCF** is the largest whole number that divides evenly into each of the numbers.

**FACTORS** are the **numbers that you multiply to get another number**. [ 3 X 5 = 15 where the factors are 3 and 5]

To get the greatest common factor, one can use two methods:

- First is to list all the factors of the given numbers. The list the
**common factors**or the same factors for these given numbers. When this has been done, choose the biggest number among the common factors.

ex: 30 = **1**, **2**, 3, **5**, 6, **10**, 15, 30

20 = **1**, **2**, 4, **5**, **10**, 20

**The common factors for 30 and 20 are 1,2, 5 and 10 therefore the greatest common factor is 10**.

- Another method for finding the greatest common factor is
**listing down the prime factors**. After listing the prime factors, multiply these prime factors.

**PRIME FACTORS** are numbers that can only be multiplied by 1 and itself [ex: 2,3,5,7,11…]

The prime factors for 30 are 5 x 3 x 2

The prime factors for 20 are 5 x 2 x 2

The prime factorization of 30 and 20 have *one* **5** and *one* **2** in common. Multiply these common prime factors and you get the greatest common factor.

**5 x 2 = 10**

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