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FACTORS AND MULTIPLES
A FACTOR; is a number that divides exactly into another number. Examples: 1,2,3 and
6 are
factors of the # 6.
PRIME NUMBERS: Are numbers that have exactly 2 factors, 1 and the #
itself
Examples of prime numbers are: 2,3,5,7,11,37,41 etc.
EXCEPT FOR THE #2, ALL PRIME NUMBERS ARE ODD #'S.
COMPOSITE NUMBERS: are numbers that have more than 2 factors. Examples: 4,
6, 9, 10 are composite numbers.
When we find the factors that are the same for two different numbers, they
are called
COMMON FACTORS
FIND THE COMMON FACTORS THAT THE NUMBERS 12 AND 16
SHARE.
12
(
)
16
(
)
THE GREATEST COMMON FACTOR: is the largest factor that both numbers have in
common
THE GREATEST COMMON FACTOR (GCF) THAT THE NUMBERS 12 AND 16
SHARE IS _________________________
PRIME NUMBERS AND
FACTORS
FACTORS are numbers
that will divide into another number without resulting in a
decimal
PRIME NUMBERS have exactly 2 factors, itself and 1.
17, 29
Examples
11, 5,
COMPOSITE NUMBERS have more than 2 factors. Examples: 4, 10, 15,
50
All numbers except 1 can be written as the product of two different
factors.
The number 36 can be written as: 1x36, 2x18, 3x12, 4x9, 6x6.
So, the factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18 and 36.
RECALL:
)
36: (
Some of these factors are prime numbers, so they are considered prime factors
of the # 36
PRIME FACTORIZATION: To find the prime factors of any
number, think of what two numbers (factors) you can
multiply together to get that number. You then continue
doing the same thing with the new numbers (factors) until
you cannot find any more factors. What you are left with
are the PRIME FACTORS of the number.
36
USE A FACTOR TREE
You may find that there are more than one of the same factors on the bottom of
your tree. That's fine. to show a number as a PRODUCT OF IT'S PRIME
FACTORS, you list all the prime factors multiplied by each other. You may be
able to simplify the sentence if there are prime factors that repeat.
36
36
9X4
12 X 3
3X 3 X 2 X 2
6X2 X 3
2 X 3 X2 X 3
3 X2
2
2
3 X2
2
36
2
MULTIPLES: ARE FOUND BY MULTIPLYING THE NUMBER BY 1, BY 2, BY 3, BY4,
ETC.
THE MULTIPLES OF THE NUMBER 9 ARE: 9, 18, 27, 36,
_____,_____,_____
COMMON MULTIPLES: ARE FOUND WHEN TWO NUMBERS HAVE A MULTIPLE
THAT IS THE SAME FOR BOTH.
EXAMPLE: FIND THE MULTIPLES OF THE NUMBERS 6 AND 8
6
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72
8
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
24, 48, AND 72 ARE COMMON TO BOTH LISTS, SO
THEY ARE CALLED COMMON MULTIPLES.
THE LOWEST COMMON MULTIPLE (LCM) IS THE FIRST NUMBER THAT IS
COMMON TO BOTH NUMBERS. IN THE EXAMPLE ABOVE IT IS THE # 24
LIST THE PRIME FACTORS FOR 50
WRITE 16 AS A PRODUCT OF ITS PRIME
FACTORS
FIND ALL COMMON FACTORS OF 48, 64
48
)
64
)
(
(
FIND THE FIRST 3 COMMON MULTIPLES OF 12,
16
12
16
A NUMBER HAS 2, 3, AND 5 AS FACTORS.
A) WHICH IS THE LCM FOR THESE 3 NUMBERS?
2
3
5
B) FIND TWO MORE NUMBERS WITH THESE SAME
FACTORS