4.4 Prime Factorization

Prime Factorization

Prime factorization = write as product of primes

Ex 1) Find prime factorization of 936936

2 468

2 234

2 117

3 39

3 13

936 = 2 • 2 • 2 • 3 • 3 • 13

= 23 • 32 • 13

Vocabulary

GCF = Greatest Common Factor– Biggest number that divides evenly into all three

numbers

LCM = Least Common Multiple– Smallest number that can be divided by all three

numbers

(smaller # than orig)

(larger # than orig)

Ex 2) Find the GCF and LCM of 72, 108, 126

72 108 1262369 4

GCF: 2 • 9 = 18

1st: Find a number that divides evenly into all the numbers2nd: Continue until you can’t find any more numbers

Ladder Method

54 636 7

Ex 2) Find the GCF and LCM of 72, 108, 126

72 108 126

Ladder Method

3rd: Find a number that divides evenly into at least 2 #4th: Continue until you can’t find any more numbers

236 54 639 4 6 72 2

LCM: 2 • 9 • 2 • 2 • 3 • 7 = 1512

3 7If it doesn’t go in, just bring # down

Ex 3) Find the GCF and LCM of 48u2v2 and 60uv3w

48u2v2 60uv3w124u2v2 uv2

4u

GCF: 12uv2

LCM: 12uv2 • 4u • 5vw = 240u2v3w

5uv3w5vw

Ex 4) Find the GCF and LCM of 30, 35, 36, 42

30 35 36 42130 35 36 425661

LCM: 5 • 6 • 7 • 6 = 1260GCF: 1

71

7 36 427 6 71 6 1

TOO: Find the GCF and LCM

1) 100, 120, 90

2) 32x3y3, 120xy4, 42x2y3

Answers:

1) GCF: 10, LCM: 1800

2) GCF: 2xy3, LCM: 3360x3y4

Homework

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