GREATEST COMMON FACTOR

The greatest common factor (GCF) of 2 or more numbers is 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.

Find the GCF of 42 and 60. 2 60 2 3 30 2 7 7  15 3 1 5 5 1 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!

Find the Greatest Common Factor (GCF) of 16 and 24. 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. Find the Greatest Common Factor (GCF) of 16 and 24. 16 24 1 × 16 1 × 24 2 × 8 2 × 12 4 × 4 3 × 8 4 × 6 The GCF of 16 and 24 is 8 © 2007 M. Tallman

Greatest Common Factor 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 HCF of : 2x3x5 and 2x3x7 2x3x5x7 and 2x2x3x11 3) 2x2x3x5 and 2x2x3x11 4) 2x2x2x5x7 and 2x2x2x5x11 5) 2x2x2x7x7 and 2x2x2x7x11

GCF Example: Applying what 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? 2 l 72 2 l 90 2 l 36 3 l 45 2 l 18 3 l 15 3 l 9 5 l 5 3 l 3 1 1 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

YOUR TURN! 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?

LEAST COMON MULTIPLE

The least common multiple of 2 or more numbers is the smallest number that is common between two lists of multiples.

Write the common and non common factors with the greatest exponents Find the LCM of 42 and 60. 2 60 2 3 30 2 7 7  15 3 1 5 5 1 Write the common and non common factors with the greatest exponents The LCM of 42 and 60 is 420.

Find the least common multiple (LCM). Method 2: Use a list. 3, 4, and 9 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, . . . List multiples of 3, 4, and 9. 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, … Find the smallest number that is in all the lists. 9: 9, 18, 27, 36, 45, . . . The least common multiple of 3, 4, and 9 is 36.

Least Common Multiple Find the LCM of the following 2 and 5 3 and 8 2, 3 and 4 4. 3 and 9 5. 2,4 and 6

1. 2x5 and 5x5 2. 2x2x3 and 2x2x5 3. 2x2x3 and 2x7 4.2x2x2 and 2x7 Find the LCM of 1. 2x5 and 5x5 2. 2x2x3 and 2x2x5 3. 2x2x3 and 2x7 4.2x2x2 and 2x7 5. 2x2x5 and 5x5

LCM Example: Applying what we have learned… 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 3 8 = 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.

YOUR TURN 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?