4, 6, 8, 9, 10, 12, 14, 15, 16, . . .
12 ÷ 3 = 4 The number 3 is, therefore, a factor
of the number 12. Other factors of
■ The number 1 is neither prime nor composite.
12 are 1, 2, 4, 6, and 12.
Prime Factorization
The SAT will ask you to combine several skills at once.
The common factor of two numbers are the fac-
tors that both numbers have in common.
One example of this, called prime factorization, is a
process of breaking down factors into prime numbers.
Example:
The factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.
Examples:
18 = 9 × 2 The number 9 can also be written
The factors of 18 = 1, 2, 3, 6, 9, and 18.
as 3 × 3. So, the prime factoriza-
From the above, you can see that the common
tion of 18 is:
18 = 3 × 3 × 2
factors of 24 and 18 are 1, 2, 3, and 6. From this list, we
can also determine that the greatest common factor of
This can also be demonstrated with the factors
6 and 3: 18 = 6 × 3
24 and 18 is 6. Determining the greatest common fac-
Because we know that 6 is equal to 2 × 3, we can
tor is useful for reducing fractions.
Any number that can be obtained by multiplying a
write: 18 = 2 × 3 × 3
number x by a positive integer is called a multiple of x.
According to the commutative law, we know
that 3 × 3 × 2 = 2 × 3 × 3.
Some multiples of 5 are: 5, 10, 15, 20, 25, 30, 35,
Number Lines and Signed
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