Using Prime Factorization Objective: To find the GCF and LCM of integers and monomials

Prime Numbers An integer greater than 1 whose only factors are its self and one. Examples: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29…} Real life application: cryptography (code breaking)

Example: Find the prime factorization of 432 432 = 216 • 2 = 108 • 2 • 2 = 54 • 2 • 2 • 2 = 27 • 2 • 2 • 2 • 2 = 9 • 3 • 2 • 2 • 2 • 2 = 3 • 3 • 3 • 2 • 2 • 2 • 2 =33 • 24

Greatest Common Factor (GCF) The greatest integer that is a factor of each integer. Example: find the GCF of 27 and 117 27 = 3 • 3 • 3, 117 = 13 • 3 • 3 GCF = 3 • 3 = 9

Least Common Multiple (LCM) Least positive integer having each as a factor Example: Find the least common multiple of 27 and 117 27 = 3 • 3 • 3 = 33, 117 = 13 • 3 • 3 = 13 • 32 Take the largest factors of each number LCM = 33 • 13 = 351

Try These! find the GCF and LCM 16a4b3 and 12a2b 21a2b5, 14a3b3, and 35a2b2 4, 240 Solution 11, 330 Solution 5, 6300 Solution 4a2b, 48a4b3 Solution 7a2b2, 210a3b5 Solution End Show

80 and 12 80 = 40 • 2 80 = 20 • 2 • 2 80 = 10 • 2 • 2 • 2 80 = 5 • 2 • 2 • 2 • 2 80 = 5 • 24 12 = 6 • 2 12 = 3 • 2 • 2 12 = 3 • 22 GCF = 4 LCM = 5 • 24 • 3 = 240 Back to Try These!

110 and 33 110 = 11 • 5 • 2 33= 3 • 11 GCF = 11 LCM = 11 • 5 • 2 • 3 LCM = 330 Back to Try These!

45, 100, and 70 45 = 32 • 5 100 = 52 • 22 70 = 7 • 5 • 2 GCF = 5 LCM = 6300 Back to Try These!

16a4b3 and 12a2b 16a4b3 = 24 • a4 • b3 12a2b = 22 • 3 • a2 • b GCF = 22 • a2 • b GCF = 4a2b LCM = 24 • 3 • a4 • b3 LCM = 48a4b3 Back to Try These!

21a2b5, 14a3b3, and 35a2b2 21a2b5 = 7•3•a2•b5 14a3b3 = 7•2•a3•b3 GCF = 7•a2•b=7a2b LCM = 7•5•2•3•a3•b5 LCM = 210a3b5 Back to Try These!