You may be wondering why you have to learn about greatest common factor (GCF) and least common multiples (LCM). Both of these are needed to perform the different operations when doing fractions. Understanding both are critical for not only fractions but also in some problems you need to solve.
Greatest Common Factor
The highest number that divides exactly into two or more numbers.
It is the "greatest" thing for simplifying fractions!
![Picture](/uploads/1/1/9/9/119951240/greatest-common-factor_orig.jpg)
What is a "Common Factor" ?
Let's say you have worked out the factors of 12 and 30:
Factors of 12 are 1, 2, 3, 4, 6, 12
Factors of 16 are 1, 2, 4, 8, 16
Then the common factors are those that are found in both lists:
It is a common factor when it is a factor of two or more numbers. (It is then "common to" those numbers.)
The GREATEST common factor is just that...the greatest one.
Let's say you have worked out the factors of 12 and 30:
Factors of 12 are 1, 2, 3, 4, 6, 12
Factors of 16 are 1, 2, 4, 8, 16
Then the common factors are those that are found in both lists:
- Notice that 1, 2, and 4 appear in both lists?
- So, the common factors of 12 and 30 are: 1, 2, and 4
It is a common factor when it is a factor of two or more numbers. (It is then "common to" those numbers.)
The GREATEST common factor is just that...the greatest one.