Factors, Common Factors & Greatest Common Factors (GCF) 6.NS.4 Factors, Common Factors & Greatest Common Factors (GCF) This presentation demonstrates the new capabilities of PowerPoint and it is best viewed in Slide Show. These slides are designed to give you great ideas for the presentations you’ll create in PowerPoint 2010! For more sample templates, click the File tab, and then on the New tab, click Sample Templates.

GREATEST COMMON FACTORS Key Words: factor, product, multiple, composite number, prime number, prime factorization, & factor tree 1 FACTORS 2 COMMON FACTORS 3 GREATEST COMMON FACTORS (GCF)

A number that is multiplied by another number to find a produCT A number that is multiplied by another number to find a produCT. 4 x 7 = 28 ←Product 4 and 7 are both factors 4 and 7 are factors of 28, 4 x 7 = 28. 2 and 14 are also factors of 28, 2 x 14 =28 1 and 28 are factors of 28, 1 x 28 = 28. (1, 2, 4, 7, 14, and 28 are factors of 28)

Common factor: a number that is a factor of two or more numbers Here are the factors of 30; 1, 2, 3, 5, 6, 10, 15 & 30 Here are the factors of 50: 1, 2, 5, 10, 25, & 50 The common factors of 30 and 50 are: 2, 5, and 10 10 is the greatest common factor (GCF) of 30 and 50

Using prime factorization to find GCF 30 50 2 15 2 25 We use common factors to simplify fractions. 3 5 5 5 2 5 3 5 30 and 50 each have a 2 and a 5, so I put a 2 and a 5 in the middle. The 30 had a 3 left over and the 50 had a 5 left over to put into the outside non-sharing section of the Venn Diagram.

Find the Greatest Common Factor (GCF) of 36 and 48 write the factors in sequence order: 1, 2, 3, 4, 6, 9, 12, 18 & 36 48: (1 & 48), (2 & 24), (3 & 16), (4 & 12), (6 & 8), or in sequential order: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 The Common Factors of 36 & 48 are: 2, 3, 4, 6, 12. The GCF is 12

Using Factors in the Real-World! Nolan wants to build a dog pen to house his new dog, Max. The area he can use is 42 square feet. What possible measurements can he use for the dog pen? Which measurements are best? Be prepared to explain your solution! Factors of 42 are: 1 and 42, 2 and 21, 3 and 14, and 6 and 7.

Composite Number: All numbers that have a factor pair other than 1 and itself. Examples include, 4, 6, 8, 9, 10, 12, 15, …….. Prime Number: All numbers that only have 1 and itself as factors. Examples include, 3, 7, 11, 13, 17 19…… Why no Even numbers?????

Multiples, Common Multiples and Least Common Multiple Multiple: The product of a given whole number and another whole number Multiples of 3 are: 1 x 3 = 3, 2 x 3 = 6, 3 x 3 = 9, 3 x 4 = 12 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 3 3, 36, 39, 42, 45……… continues infinitely

COMMON MULTIPLES AND (LCM) We need to find common multiple and Least Common Multiple when finding common denominators or when buying items at the store, such as hotdogs and buns. The hotdogs I buy come 8 in a pack. The buns I buy come in packs of 10. What common number does 8 and 10 share (common multiple)? 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110 Some common numbers of 8 and 10 are: 40, 80, 120, 160, 200, Do you see a pattern? Which is the lowest number 8 and 10 have in common? Yes, 40 is the Least Common Multiple. I would need to buy 5 packs of hotdogs and 4 packs of hotdog buns to have the same amount of each. Remember multiples can go on for ever. The Least Common Multiple is the first or lowest number 2 or more numbers have in common.

Find 5 common multiples of 6 and 8 Find 5 common multiples of 6 and 8. Find the Least Common Multiple of 6 and 8. 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120 Common Multiples of 6 and 8 are: 24, 48, 72, 96, 120. Least Common Multiple (LCM) of 6 and 8 is 24

Other Resources mailto:www.khanacademy.org/math/arithmetic/factors-multiples mailto:http://www.math.com/school/subject1/lessons/S1U3L1GL.html

30 2 15 3 5

Dividing Fractions