the largest number that can divide into all of the numbers.

Find the GCF of 42 and 60. Write the prime factorization of

each number.

What prime factors do the numbers have in common?

Multiply those numbers with the lowest exponents .The GCF is 2 x 3 = 6

6 is the largest number that can go into 42 and 60!

42 2 60 2433 30 2 7 7  15 3

1 5 5 1

© 2007 M. Tallman

8

Find the Greatest Common Factor (GCF) of 16 and 24.

16×××

Step 1: Make a “T-Chart” for both numbers.

Step 2: Look for common factors between both numbers.

Step 3: Circle the greatest factor that both numbers have in common.

Step 4: This is the GCF.

1 162 84 4

24××

1 242 12

The GCF of 16 and 24 is 8

×3×4 6

Find the GCF of 12 and 18 18 and 27 24 and 30 36 and 45 24 and 36 16, 32 and 40 18,27 and 36

Find the GCF of :

1) 2x3x5 and 2x3x7 2) 2x3x5x7 and 2x2x3x11 3) 2x2x3x5 and 2x2x3x11 4) 2x2x2x5x7 and 2x2x2x5x115) 2x2x2x7x7 and 2x2x2x7x11

2 l 72 2 l 902 l 36 3 l 452 l 18 3 l 153 l 9 5 l 53 l 3 1 1

72 = 2 x 2 x 2 x 3 x 390 = 2 x 3 x 3 x 5

GCF = 2 x 3 x 3 = 18

Samantha should cut each piece to be 18 inches wide

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?

1. Mrs. Evans has 120 crayons and 30 pieces of paper to give to her students. What is the largest # of students she can have in her class so that each student gets equal #

of crayons and equal # of paper.

2. I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row?

the smallest number that is common between two lists of multiples.

Write the common and non common factors with the greatest exponents

The LCM of 42 and 60 is 420.

4242 2 60 22 60 243433 30 23 30 2 7 77 7   15 3 15 3

1 5 51 5 5 1 1

Find the least common multiple (LCM).

Method 2: Use a list.

3, 4, and 93: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, . . .

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, …

9: 9, 18, 27, 36, 45, . . .

The least common multiple of 3, 4, and 9 is 36.

List multiples of 3, 4, and 9.

Find the smallest number that is in all the lists.

Find the LCM of the following

1. 2 and 52. 3 and 83. 2, 3 and 44. 3 and 95. 2,4 and 6

1. 2x5 and 5x52. 2x2x3 and 2x2x5 3. 2x2x3 and 2x74.2x2x2 and 2x7 5. 2x2x5 and 5x5

Ben exercises every 12 days and Isabel every 8 days. Ben and Isabel both exercised today. How many days will it be until they exercise together again?

2 l 12 2 l 8 2 l 6 2 l 4 3 l 3 2 l 2 1 1 12 = 2 x 2 x 38 = 2 x 2 x 2

LCM = 2 x 2 x 2 x 3 = 24

Ben and Isabel would exercise on the same day every 24 days.

1.Two bikers are riding a circular path. The first rider completes a round in 12 minutes. The second rider completes a round in 18 minutes. If they both started at the same place and time and go in the same direction, after how many minutes will they meet again at the starting point?

2. Sean has 8-inch pieces of toy train track and Ruth has 18-inch pieces of train track. How many of each piece would each child need to build tracks that are equal in length?