Sat math Essentials

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N U M B E R S A N D O P E R AT I O N S R E V I E W
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4 8

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Factors
Factors
of a number are whole numbers that, when divided into the original number, result in a quotient that is
a whole number.
Example
The factors of 18 are 1, 2, 3, 6, 9, and 18 because these are the only whole numbers that divide evenly into 18.
The 
common factors
of two or more numbers are the factors that the numbers have in common. The 
great-
est common factor
of two or more numbers is the largest of all the common factors. Determining the greatest
common factor is useful for reducing fractions.
Examples
The 
factors
of 28 are 1, 2, 4, 7, 14, and 28.
The 
factors
of 21 are 1, 3, 7, and 21.
The 
common factors
of 28 and 21 are therefore 1 and 7 because they are factors of both 28 and 21.
The 
greatest common factor
of 28 and 21 is therefore 7. It is the largest factor shared by 28 and 21.
Practice Question
What are the common factors of 48 and 36?
a.
1, 2, and 3
b.
1, 2, 3, and 6
c.
1, 2, 3, 6, and 12
d.
1, 2, 3, 6, 8, and 12
e.
1, 2, 3, 4, 6, 8, and 12
Answer
c.
The factors of 48 are 1, 2, 3, 6, 8, 12, 24, and 48. The factors of 36 are 1, 2, 3, 6, 12, 18, and 36. Therefore,
their common factors—the factors they share—are 1, 2, 3, 6, and 12.
M u l t i p l e s
Any number that can be obtained by multiplying a number 
x
by a whole number is called a 
multiple
of
x
.
Examples
Multiples of
x
include 1
x
, 2
x
, 3
x
, 4
x
, 5
x
, 6
x
, 7
x
, 8
x
. . .
Multiples of 5 include 5, 10, 15, 20, 25, 30, 35, 40 . . .
Multiples of 8 include 8, 16, 24, 32, 40, 48, 56, 64 . . .
The