4.2
Greatest Common Factor (GCF)
Factors: numbers multiplied together to make a product. 5 x 8 = 40
5n
(factors)
= 40
(product)
Common Factors
A number that is a factor of both m and n is a common factor of m and n. The
largest factor is called the greatest common factor or GCF.
Ex.1 Find the GCF.
12 –
18 –
Common Factors GCF =
Ex.2 Find the GCF of 27 and 45 and 90.
27 –
45 –
90 –
GCF =
Ex.3 GCF (180 , 378)
For larger numbers, begin by writing the prime factorization of each.
After prime factorization, we multiply the common factors to get the Greatest
Common Factor.
Check to see that your answer is a divisor of the two numbers.
Ex.4 The concept of GCF also applies to algebraic expressions.
GCF ( 18 x 2 y,12 xy )
18x 2 y -
12xy –
GCF =
Two numbers are relatively prime if their GCF is 1.
Ex.5 Are 8 and 21 relatively prime?
8–
21 –
Relatively Prime =
Ex.6 a) GCF ( 135 , 225)
b) GCF (36 x 2 y 3 z, 48 xy 2 z )