PRIME FACTORIZATION

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PRIME FACTORIZATION
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PRIME FACTORIZATION

• Every composite number can be expressed as a
  product of prime numbers. This is called the
  prime factorization of a number.

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PRIME FACTORIZATION

• To find the prime factorization of a number, you
  can use a factor tree.

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FACTOR TREES
36

6 x 6


2 x 3
2 x 3
or 2² x 3²
36 2 x 2 x 3 x 3
5
FACTOR TREES
36

3 x 12

3 x 4

2 x 2
or 2² x 3²
36 2 x 2 x 3 x 3
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FACTOR TREES
9

3 x 3
9 3 x 3
or 3²
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FACTOR TREES
21

3 x 7
21 3 x 7
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FACTOR TREES
100

10 x 10


2 x 5
2 x 5
or 2² x 5²
100 2 x 2 x 5 x 5
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PRIME FACTORIZATION

• To find the prime factorization of a number, you
  can use a factor ladder.

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FACTOR LADDERS
Begin with the least prime number that is a
factor. Repeat until the quotient is prime.
?
36
2
?
18
2
?
3
9
3
or 2² x 3²
36 2 x 2 x 3 x 3
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FACTOR LADDERS
Begin with the least prime number that is a
factor. Repeat until the quotient is prime.
?
60
2
?
30
2
?
3
15
5
or 2² x 3 x 5
60 2 x 2 x 3 x 5
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FACTOR LADDERS
?
Begin with the least prime number that is a
factor. Repeat until the quotient is prime.
45
3
?
15
3
5
or 3² x 5
45 3 x 3 x 5
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FACTOR LADDERS
Begin with the least prime number that is a
factor. Repeat until the quotient is prime.
?
125
5
?
25
5
5
or 5³
125 5 x 5 x 5