Greatest Common Factor 6.1.1.6 Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions.

I can… Find the greatest common factor of 2 or more numbers Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

Let’s Review What are factors? Numbers multiplied together in a multiplication problem.

Greatest Common Factor (GCF) The greatest common factor is the largest factor that two numbers share. 3 methods Factor List Factor Tree Upside Down Cake Method

Greatest Common Factor (GCF) Let’s find the GCF of 12 and 42 using all 3 methods.

12 42 1 x 12 1 x 42 Factors of 12: 1, 2, 3, 4, 6,12 2 x 21 2 x 6 3 x 14 3 x 4 4 x ?? 4 x 3 Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 5 x ?? 6 x 7 7 x 6 Common Factors: 1, 2, 3, 6 Greatest Common Factor: 6

Prime Factorization 42 12 2 x 21 2 x 6 2 x 3 x 7 2 x 2 x 3 2 x 3 = 6

Upside Down Cake Method 12 42 3 2 4 14 2 7 3 X 2 = 6

What is the GCF of 18 and 27? 18 27 Factors of 18: 1, 2, 3, 6, 9, 18 1 x 18 1 x 27 2 x ? 2 x 9 3 x 9 3 x 6 Factors of 27: 1, 3, 9, 27 4 x ? 5 x ? 4 x ? 6 x ? 5 x ? 7 x ? Common Factors: 1, 3, 9 8 x ? 6 x 3 9 x 3 GCF: 9

Prime Factorization 27 18 3 x 9 2 x 9 3 x 3 x 3 2 x 3 x 3 3 x 3 = 9

Upside Down Cake Method 18 27 3 3 6 9 2 3 3 X 3 = 9

What is the GCF of 48 and 60? Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 48 60 1 x 48 1 x 60 2 x 30 2 x 24 3 x 20 3 x 16 4 x 15 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 4 x 12 5 x 12 6 x 8 6 x 10 Common Factors: 1, 2, 3, 4, 6, 12 GCF: 12

Prime Factorization 48 60 8 x 6 2 x 30 2 x 4 x 2 x 3 2 x 3 x 10 2 x 2 x 2 x 2 x 3 2 x 3 x 2 x 5 2 x 2 x 3 = 12

Upside Down Cake Method 48 60 3 4 16 20 4 5 3 X 4 = 12

Your Turn Find the GCF of 14 and 35 (Pick your method) 7

Your Turn Find the GCF of 12, 20, and 30 (Pick your method) 2

Your Turn Find the GCF of 24, 48, and 72 (Pick your method) 2

Your Turn What is the greatest number of sections you can have if you have 72 marigolds and 144 petunias? 72

I can… Find the greatest common factor of 2 or more numbers Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

Daily Check 5.2 in your math notebook Find the GCF for each group of numbers 45, 105 36, 54, 90 72, 120, 280 56, 196, 252 An antiques dealer has 35 rings and 75 pins to display. The display should have equal sized rows, and pins and rings should not appear in the same row. How many items should appear in each row?