As mentioned earlier,
factors of a number are whole numbers that when multiplied together yield the number.
Example 1
What are the factors of 10?
10 = 2 × 5
and 10 = 1 × 10
So the factors of 10 are 1, 2, 5, and 10.
Example 2
What are the factors of 24?
Therefore, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Common factors
Common factors are those factors that are the same for two or more numbers.
Example 3
What are the common factors of 6 and 8?
1 and 2 are common factors of 6 and 8.
Note: Some numbers may have many common factors.
Example 4
What are the common factors of 24 and 36?
Thus, the common factors of 24 and 36 are 1, 2, 3, 4, 6, and 12.
Greatest common factor
The greatest common factor (GCF) is the largest factor common to two or more numbers.
Example 5
What is the greatest common factor of 12 and 30?
Notice that, although 1, 2, 3, and 6 are all common factors of 12 and 30, only 6 is the greatest common factor.