Algebra 1 Common Core Student Edition, Grade 8-9

Fact o r s an d M u l t i p l es

A com m on factor is a n u m b e r th a t is a factor of two or m ore num bers. The greatest

com m on factor (GCF) is th e greatest n u m b e r th a t is a com m on factor of two or

m ore num bers.

Ex a m p l e 1

Find the GCF o f 24 and 64.

Method 1 List all th e factors of each num ber.

Factors of 24 1 ,2 ,3 ,4 ,6 ,8 ,1 2 ,2 4

Factors of 64 1,2, 4, 8,1 6 ,3 2 , 64

The GCF of 24 an d 64 is 8.

Find the common factors: 1, 2 ,4 , 8.

The greatest common factor is 8.

Method 2 Use th e prim e factorization of each num ber.

24 = 2 • 2 • 2 • 3 Find the prime factorization o f each number.

64 = 2,2*2,2*2*2

GCF = 2 • 2 • 2 = 8 The product o f the common prime factors is the GCF.

A com m on m ultiple is a n u m b e r th at is a m ultiple of two or m ore n um bers. The least

com m on m ultiple (LCM) is th e least n u m b e r th at is a co m m o n m ultiple of two or

m ore num bers.

Ex a m p l e 2

Find the LCM o f 12 and 18.

Method 1 List th e m ultiples of each num ber.

Multiples of 12 12, 24, 36,...

Multiples of 18 18, 36,...

The LCM of 12 an d 18 is 36.

Method 2 Use th e p rim e factorization of each num ber.

12 = 2 • 2 • 3

18 = 2 • 3 • 3

LCM = 2 • 2 • 3 • 3 = 36

List the m ultiples o f each number until you find

the first common multiple.

Use each prime factor the greatest

number o f tim es it appears in either number.

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Ex e r c i se s

Find the GCF o f each set of numbers.

1. 12 an d 22 2. 7 a n d 21

Find the LCM o f each set of numbers.

5. 16 an d 20 6. 14 a n d 21
   3. 24 an d 48
   7. 11 an d 33
   4. 42, 63, an d 105

8. 6 , 7, a n d 12

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