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Prime Factorization
7th Grade Math
Prime Factorization Of a Number


A prime number is a counting number that only
has two factors, itself and one. Counting numbers
which have more than two factors (such as six,
whose factors are 1, 2, 3 and 6), are said to be
composite numbers. When a composite
number is written as a product of all of its prime
factors, we have the prime factorization of the
number.
There are several different methods that can be
utilized for the prime factorization of a number.
Using Division


Prime factors can
be found using
division.
Keep dividing until
you have all prime
numbers. The
prime factors of 78
are 2, 3, 13.
39
2 78
13
3 39
Remember the Divisibility Rules
If the last digit is even, the number is
divisible by 2.
 If the last digit is a 5 or a 0, the number is
divisible by 5.
 If the number ends in 0, it is divisible by
10.
 If the sum of the digits is divisible by 3,
the number is also.
 If the last two digits form a number
divisible by 4, the number is also.

More divisibility rules…
If the number is divisible by both 3 and 2,
it is also divisible by 6.
 Take the last digit, double it, and subtract
it from the rest of the number; if the
answer is divisible by 7 (including 0), then
the number is also.
 If the last three digits form a number
divisible by 8, then the whole number is
also divisible by 8.
 If the sum of the digits is divisible by 9,
the number is also.

 Using
the Factor Tree
78
/ \
/
2
/
/
2 x
\
x
39
/
/
3 x
\
\
13
Exponents
72
/

\
8 x 9
/ \
/ \
2x4x3x3
/ / \ \ \
2 x2 x2x3x3
Another key idea in
writing the prime
factorization of a number
is an understanding of
exponents. An exponent
tells how many times the
base is used as a factor.
72 = 23 x 32
Let’s Try a Factor Tree!
84
/ \
2 x 42
/
/ \
2 x 2 x 21
/
/
/ \
2 x 2 3 x 7
What is the final factorization?
22 x 3 x 7 = 84
Factor Trees do not look the same for the same number,
but the final answer is the same.
72
/ \
8 x 9
/ \
/ \
2x4x3x3
/ \
2 x2 x 2x 3x3
72
/ \
2 x 36
/ /
\
2 x 2 x 18
/ /
/ \
2x 2 x 2 x 9
/
/
/
/ \
2 x 2 x2x 3x 3
Greatest Common Factors
One method to find greatest common
factors is to list the factors of each
number. The largest number is the
greatest common factor.
 Let’s find the factors of 72 and 84.
72
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

84
1, 2, 3, 4, 6, 12, 14, 21, 28, 42, 84
Prime Factorization is helpful for finding
greatest common factors.
72
/ \
8 x 9
/ \
/ \
2x4x3x3
/ \
2 x2 x 2x 3x3
Take the common prime
factors of each number
and multiply to find the
greatest common factor.
84
/ \
2 x 42
/
/ \
2 x 2 x 21
/
/
/ \
2 x 2
3 x 7
2 x 2 x 3 = 12
Resources
IXL.Com – Sixth Grade – N.5 Prime
Factorization
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http://www.ixl.com/math/grade6/prime-factorization