14 01 Greatest Common Factor Factors are numbers

14. 01 Greatest Common Factor

Factors are numbers that are being multiplied. To find the factors of a number, find all the pairs of factors that multiply to that number. or Divide the number by all the whole numbers, if the factor divides evenly then the factor and the quotient are factors of the number. Keep dividing until the factors repeat. Find the factors of 48 1 · 48 2 · 24 3 · 16 4 · 12 6· 8 Factors { 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 , 48 } Find the factors of 72 1 · 72 2 · 36 3 · 24 4 · 18 6 · 12 8· 9 Factors { 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 18 , 24 , 36 , 72 }

The largest factor that is common to two or more numbers is called the Greatest Common Factor (GCF). To find the GCF of two numbers, find all the factors of both numbers and find the largest factor common to both numbers. Find the GCF of: 24 and 30 Factors of 24: 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24 Factors of 30: 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30 The common factors are: 1, 2, 3, 6 GCF = 6

Find the GCF of: 28 and 42 Factors of 28: 1 , 2 , 4 , 7 , 14 , 28 Factors of 42: 1 , 2 , 3 , 6 , 7 , 14 , 21 , 42 The common factors are: 1 , 2 , 7 , 14 GCF = 14 Find the GCF of: 15 and Factors of 15: 1 , 3 , 5 , 15 1 , 2 , 4 , 8 , 16 Factors of 16: The common factors are: 1 GCF = 1 16

One can also find the GCF of monomials. To find the GCF of monomials, find the GCF of the coefficients and find the GCF of the variables. Find the GCF of: 18 x 3 and Factors of 18: Factors of 12: 1 , 2 , 3 , 6 , 9 , 18 1 , 2 , 3 , 4 , 6 , 12 Factors of x 3: Factors of x 2: x , x 2 , x 3 x , x 2 GCF = 6 x 2 12 x 2

Try This: Find the GCF of: 36 and 54 Factors of 36: 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36 Factors of 54: 1 , 2 , 3 , 6 , 9 , 18 , 27 , 54 GCF = 18 Find the GCF of: Factors of 9: 9 x 27 x 2 1, 3, 9 Factors of 27: 1 , 3 , 9 , 27 Factors of x: Factors of x 2: and x x , x 2 GCF = 9 x