Finding the Greatest common factor (gcf) 6.NS.B4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).. Finding the Greatest common factor (gcf)

Vocabulary Greatest Common Factor – the largest factor shared by 2 or more whole numbers

Make a list Find the GCF of 16 and 24 16: 1 x 16, 2 x 8, 4 x 4 24: 1 x 24, 2 x 12, 3 x 8, 4 x 6 GCF = 8

Make a list Find the GCF of 36 and 72 36: 72: GCF = 36

Make a List Method Advantages: Disadvantages: Quick to think of multiplication facts Disadvantages: With larger numbers, a list may get very long Easy to forget a pair of factors (which may contain the GCF)

Use the ladder/stairs Put both numbers inside the ladder Pull out a common factor(2, 3, and 5 are used most) Continue dividing until the only common factor is 1 Multiply the numbers that are in front of each step together to get the GCF

Use the ladder/stairs Find the GCF of 16 and 24 16 24 16 24 2 Multiply 2 x 2 x 2 8 12 2 GCF = 8 4 6 2 2 3

Use ladder/stairs Find the GCF of 36 and 72 36 72 36 72 2 Multiply 2 x 2 x 3 x 3 18 36 2 GCF = 36 9 18 3 3 6 3 1 2

Ladder/stair Method Advantages: Disadvantages: Quick to divide by prime numbers like 2, 3 and 5 Disadvantages: Will stop too soon which will prevent you from having all the necessary numbers Make a mistake when dividing within the ladder

Using Prime factorization to find GCF. Use a factor tree to find the prime factorization of 30 and 45. 30 45 2 15 3 15 3 5 3 5 Select all the prime numbers that both numbers have in common. They must match up. Does 2 have a match? If so, write the prime number at the bottom in a multiplication problem. Does 3 have a match? If so, write it at the bottom. Does the second 3 have a match? If so write it at the bottom. Does 5 have a match? If so, write it at the bottom. Multiplication problem: 3 * 5 = 15 The GCF of 30 and 45 is 15.

The Venn diagram use in helping with gcf. 30 45 2 3 3 5 Multiply the common factors together to get your GCF. GCF: 3 x 5 = 15

Word Problems Ms. Kline makes balloon arrangements. She has 40 balloons total: 24 yellow and 16 white. Each arrangement must have the same amount of each color. What is the greatest number of arrangements that Ms. Kline can make if every balloon is used?

Word Problems The local recreation center held a scavenger hunt. There were 15 boys and 9 girls at the event. The group was divided into the greatest number of teams possible with the same number of boys and girls on each team. How many teams were made if each person was on a team?