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4.4 Prime Factorization

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Prime Factorization Prime factorization = write as product of primes Ex 1) Find prime factorization of 936 936 2 468 2 234 2 117 3 39 3 13 936 = 2 2 2 3 3 13 = 2 3 3 2 13

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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)

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Ex 2) Find the GCF and LCM of 72, 108, 126 72 108 126 2 36 9 4 GCF: 2 9 = 18 1 st : Find a number that divides evenly into all the numbers 2 nd : Continue until you can’t find any more numbers Ladder Method 54 63 6 7

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Ex 2) Find the GCF and LCM of 72, 108, 126 72 108 126 Ladder Method 3 rd : Find a number that divides evenly into at least 2 # 4 th : Continue until you can’t find any more numbers 2 36 54 63 9 4 6 72 2 LCM: 2 9 2 2 3 7 = 1512 3 7 If it doesn’t go in, just bring # down

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Ex 3) Find the GCF and LCM of 48u 2 v 2 and 60uv 3 w 48u 2 v 2 60uv 3 w 12 4u 2 v 2 uv 2 4u GCF: 12uv 2 LCM: 12uv 2 4u 5vw = 240u 2 v 3 w 5uv 3 w 5vw

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Ex 4) Find the GCF and LCM of 30, 35, 36, 42 30 35 36 42 1 5 66 1 LCM: 5 6 7 6 = 1260 GCF: 1 7 1 7 36 42 7 6 7 1 6 1

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TOO: Find the GCF and LCM 1) 100, 120, 90 2) 32x 3 y 3, 120xy 4, 42x 2 y 3 Answers: 1) GCF: 10, LCM: 1800 2) GCF: 2xy 3, LCM: 3360x 3 y 4

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Homework # 403 Pg. 181 1 – 20 all

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