GCF Example: Applying skills that we have learned… Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips? How many strips will she have when she is done?

Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips? What do I Know: The pieces of cloth are 72 and 90 inches wide. What do I need to know: How wide should she cut the strips so that they are the largest possible equal widths? How many strips will she have when she is done?

Plan: This problem can be solved using Greatest Common Factor because we are cutting or “dividing” the strips of cloth into smaller pieces (factor) of 72 and 90. Find the GCF of 72 and 90 Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips?

GCF Word Problem Solution List Method: 1 l 72 1 l 90 2 l 362 l 45 3 l 243 l 30 4 l 185 l 18 6 l 126 l 15 8 l 9 9 l 10 Prime Factor Method 72 = 2 x 2 x 2 x 3 x 3 90 = 2 x 3 x 3 x 5. GCF = 2 x 3 x 3 = 18 Samantha should cut each piece to be 18 inches wide

How many strips will she have when she is done? 72 divided by 18 equals 4 90 divided by 18 equals 5 She will have (4 + 5) or 9 strips that are 18 inches wide when she is done.

36:1, 2, 3, 4, 6, 9, 12, 18, 36 32:1, 2, 4, 8, 16, 32 The factors 1, 2, and 4 are common to both numbers. 36:1, 2, 3, 4, 6, 9, 12, 18, 36 32:1, 2, 4, 8, 16, 32 The GCF is 4. 36:1, 2, 3, 4, 6, 9, 12, 18, 36 32:1, 2, 4, 8, 16, 32 Begin by finding the factors of 36 and 32. A band with 36 members is marching with a 32-member band. If the two bands are to have the same number of columns, what is the greatest number of columns in which you could arrange the two bands? Factors COURSE 3 LESSON 4-1 So, 4 is the greatest number of columns in which you can arrange the bands. 4-1

Find the GCF of 55 and 231. Factors COURSE 3 LESSON 4-1 Step 1 Find the prime factorization of each number. Step 2 Find the product of the common prime factors of each number. 55 = = The only common prime factor is 11. The GCF of 55 and 231 is