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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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