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6.NS.4
Factors, Common Factors &
Greatest Common Factors (GCF)
Key Words: factor, product, multiple, composite number,
prime number, prime factorization, & factor tree
FACTORS
COMMON
FACTORS
GREATEST
COMMON
FACTORS
(GCF)
A NUMBER THAT IS MULTIPLIED BY ANOTHER
NUMBER TO FIND A PRODUCT. 4 X 7 = 28
←PRODUCT
4 AND 7 ARE BOTH FACTORS
4 and 7 are factors of 28, 4 x 7 = 28.
of 28, 2 x 14 =28
1 and 28 are factors of 28, 1 x 28 = 28.
factors of 28)
2 and 14 are also factors
(1, 2, 4, 7, 14, and 28 are
Common factor: a number that is a factor of two or
more numbers
Here are the factors of 30; 1, 2, 3, 5, 6, 10, 15 & 30
Here are the factors of 50: 1, 2, 5, 10, 25, & 50
The common factors of 30 and 50 are: 2, 5, and 10
10 is the greatest common factor (GCF) of 30 and 50
We use common factors to
simplify fractions.
Using prime factorization to find GCF
30
50
2
15
3
2
5
5
3
25
2
5
5
5
30 and 50 each have a 2 and a 5, so I put a 2 and a 5 in the middle. The 30
had a 3 left over and the 50 had a 5 left over to put into the outside nonsharing section of the Venn Diagram.
Find the Greatest Common Factor (GCF) of 36 and 48
36: (1 & 36), (2 & 18), (3 & 12), (4 & 9), (6 & 6) or
write the factors in sequence order: 1, 2, 3, 4, 6, 9, 12, 18 & 36
48: (1 & 48), (2 & 24), (3 & 16), (4 & 12), (6 & 8), or
in sequential order: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The Common Factors of 36 & 48 are: 2, 3, 4, 6, 12. The GCF is 12
Using Factors in the Real-World!
Nolan wants to build a dog pen to house his new dog, Max.
The area he can use is 42 square feet.
• What possible measurements can he use for the dog pen?
• Which measurements are best?
• Be prepared to explain your solution!
Factors of 42 are: 1 and 42, 2 and 21, 3 and 14, and 6 and 7.
Composite Number: All numbers that have a factor
pair other than 1 and itself.
Examples include, 4, 6, 8, 9, 10, 12, 15, ……..
Prime Number: All numbers that only have 1
and itself as factors.
Examples include, 3, 7, 11, 13, 17 19……
Why no Even numbers?????
Multiples, Common Multiples and
Least Common Multiple
Multiple: The product of a given whole number and
another whole number
Multiples of 3 are: 1 x 3 = 3, 2 x 3 = 6, 3 x 3 = 9, 3
x 4 = 12
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 3 3, 36, 39, 42,
45……… continues infinitely
COMMON MULTIPLES AND (LCM)
We need to find common multiple and Least Common Multiple when finding common
denominators or when buying items at the store, such as hotdogs and buns. The hotdogs
I buy come 8 in a pack. The buns I buy come in packs of 10. What common number does
8 and 10 share (common multiple)?
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110
Some common numbers of 8 and 10 are: 40, 80, 120, 160, 200, Do you see a pattern?
Which is the lowest number 8 and 10 have in common? Yes, 40 is the Least Common
Multiple. I would need to buy 5 packs of hotdogs and 4 packs of hotdog buns to have the
same amount of each.
Remember multiples can go on for ever. The Least Common Multiple is the first or lowest
number 2 or more numbers have in common.
Find 5 common multiples of 6 and 8.
Find the Least Common Multiple of 6
and 8.
6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102,
108, 114, 120
8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120
Common Multiples of 6 and 8 are: 24, 48, 72, 96, 120.
Least Common Multiple (LCM) of 6 and 8 is 24
Other Resources
• mailto:www.khanacademy.org/math/
arithmetic/factors-multiples
• mailto:http://www.math.com/school
/subject1/lessons/S1U3L1GL.html
30
2
15
3
5