When to use: to reduce fractions

Skills needed: multiplication facts

**Method - Naming or Listing Factors**

Example: 12 & 36 - Find the GCF

Factors for 12: 1, 2, 3, 4, 6, 12

Factors for 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

What are the common factors? 1, 2, 3, 4, 6, 12

Which common factor is the largest? 12

Thus, the GCF for 12 & 36 is 12.

**Question: How do you list factors without missing one?**

Lets redo the above example in more detail.

Name factors of 12

Start with the factor 1. Write 1 to the left and the 2nd factor, 12 to the right with space between the two numbers. Then ask is 2 a factor of 12. If so, write 2 to the left and the matching factor, 6 to the left. Continue this pattern until 2 numbers listed from the left and right are in sequential order whether they were used as a factor or not.

Factors of 12

1-------------12

1, 2---------6, 12

1, 2,

**3------4**, 6, 12

Note: 3 and 4 are in sequential order. All factors have been listed when this happens.

Factors of 36

1-----------------36

1, 2, ---------------18, 36

1, 2, 3, ------------------12, 18, 36

1, 2, 3, 4-----------------9, 12, 18, 36

1, 2, 3, 4, X---------------9, 12, 18, 36

1, 2, 3, 4, X, 6--------------9, 12, 18, 36

1, 2, 3, 4, X, 6, X-------------9, 12, 18, 36

1, 2, 3, 4, X, 6, X,

**X**-----------

**9**, 12, 18, 36

Note: the X represents numbers that are not factors. The bold X represents 8. The number across from it is 9. Since the numbers are in sequential order, all the factors for 36 have been found.

**Application**

Reduce the fraction, 12/36.

1. Find the GCF (We know that the GCF for 12 & 36 is 12)

2. Divide the numerator and denominator by 12. (12/12 and 36/12)

3. Thus 12/36 = 1/3