Download Learn to find the greatest common factor (GCF) of a set of numbers

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:

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
2
2
2
8
24
12
4
6
2
3
Multiply 2 x 2 x 2
GCF = 8
USE LADDER/STAIRS

Find the GCF of 36 and 72
2
2
3
3
36
72
18
36
9
18
3
6
1
2
Multiply 2 x 2 x 3 x 3
GCF = 36
LADDER/STAIR METHOD

Advantages:

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
2
45
15
3
15
3
5
3
5
Select all the prime numbers that both numbers have in common.
They must match up.
1. Does 2 have a match? If so, write the prime number at the bottom
in a multiplication problem.
2. Does 3 have a match? If so, write it at the bottom.
3. Does the second 3 have a match? If so write it at the bottom.
4. 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?