Finding the Greatest Common Factor

The numbers 12 and 15 have the common factors 1 and 3.

We call 3 the greatest common factor (GCF).The notation for this is

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GCF 12,15( ) = 3

Example

Find all the common factors of 24 and 30.

① Write the factors of each number:

② List the common factors.

③ What is the greatest common factor (GCF)?

Alternate method for finding the GCF

When the number of factors is large, listing all of the factors is time consuming. An alternate approach is to write the prime factorization of each number. Then the GCF is formed by multiplying the greatest number of common (or shared) prime factors. If there are no common prime factors, the GCF=1.

Examples

1 List all the common factors of 12 and 30.

2 Find the GCF (24,30) by the alternate method.

3 Find GCF (72,90).

Multiplication Word Problems

Some word problems require that numbers be multiplied to find the answer. These word problems contain the key words discussed in Unit 1. (product, times)

Recall the key words for addition, subtraction as well from Unit 1.

Addition: sum, total, plus, in all, etc.Subtraction: subtract, difference, less, take

away, etc.

Examples

4 Roger scored 26,142 points in the first game. He scored 7 times as many in the second game. How many points did he score in all?

5 Inflation caused the price of everything to increase. The price of an item after inflation was 4 times the price before inflation. If an item cost $5.67 before inflation, what did it cost after inflation?