Common factor. Greatest common factor
Factors are numbers we can multiply together to get another number.
When we compare lists of factors of two or more numbers, any factors that are the same are the “common factors“.
Examples:
12 and 16
• The factors of 12 are: 1, 2, 3, 4, 6 and 12
• The factors of 16 are: 1, 2, 4, 8 and 16
So the common factors of 12 and 16 are: 1, 2 and 4
The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
Examples:
12, 20, and 24 have three common factors: 1, 2 and 4.
The largest is 4.
The GCF of 12, 20, and 24 is 4.
Mehtod I: using all factors.
The factors of 12 are: 1, 2, 3, 4, 6, 12.
The factors of 20 are: 1, 2, 4, 5, 10, 20.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.
So the common factors of 12, 20 and 24 are: 1, 2 and 4.
The largest is 4.
Method II: using prime factors.
The prime factors of 12 are: 2 ⋅ 2 ⋅ 3
The prime factors of 20 are: 2 ⋅ 2 ⋅ 5
The prime factors of 24 are: 2 ⋅ 2 ⋅ 2 ⋅ 3
Multipy the prime factors: 2 ⋅ 2 =4, GCF =4
Play game
https://www.sheppardsoftware.com/math/fractions/greatest-common-factor-game/