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```									Prime Factorization

Factor Trees
Find the prime factorization of 30
• Draw two “branches” off of the number.

30
Find the prime factorization of 30
• Write two numbers that are factors of 30.
*Remember: factors are the numbers multiplied together
30

6        5
Find the prime factorization of 30
• Determine if the first number is prime or
composite. (if don’t know definitions, click on the word.)

30

6        5
Prime
• The only factors of the integer are itself
and one.

• EX: 3 --- 3*1

• EX: 23 --- 23 * 1
Composite
• There are many factors for the integer.

• EX: 24 --- 1*24; 2*12; 3*8; 4*6

• EX: 32 --- 1*32; 2*16; 4*8
Find the prime factorization of 30
• Notice the 6 is NOT PRIME. It is composite. So, Draw
two “branches” off of the number and write two factors of
six at the end of each branch.

30

6        5

2       3
Find the prime factorization of 30
• The number 5 is prime, so there is no need to
draw branches from it. Just circle the number.

30

6        5

2       3
Find the prime factorization of 30
• The number 2 is prime, so there is no need to
draw branches from it. Just circle the number.

30

6        5

2       3
Find the prime factorization of 30
• The number 3 is prime, so there is no need to
draw branches from it. Just circle the number.

30

6        5

2       3
Find the prime factorization of 30
• Now that all numbers are prime, write the prime
factorization of 30.
2 * 3 *5
30

6        5

2       3
Prime Factorization
• The list of prime factors in numerical order
as products of each other.
Find the prime factorization of 81
• Draw two “branches” off of the number.

81
Find the prime factorization of 81
• Write two numbers that are factors of 81.

81

9        9
Find the prime factorization of 81
• Determine if the first number is prime or
composite.

81

9        9
Find the prime factorization of 81
• Notice the 9 is NOT PRIME. It is composite. So,
Draw two “branches” off of the number and write
two factors of nine at the end of each branch.
81

9        9

3       3
Find the prime factorization of 81
• The number 3 is prime, circle the numbers.

81

9        9

3       3
Find the prime factorization of 81
• The number 9 is not prime, so we need to draw
branches of the number nine.

81

9                9

3       3        3       3
Find the prime factorization of 81
• Now that all numbers are prime, write the prime
factorization.
3 * 3 * 3 * 3 or 34
81

9                9

3       3        3       3
Find the prime factorization.
1)   34
2)   75
3)   28
4)   120
5)   225
6)   16

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