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Prime Factorization Factor Trees

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**Find the prime factorization of 30**

Draw two “branches” off of the number. 30

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**Find the prime factorization of 30**

Write two numbers that are factors of 30. *Remember: factors are the numbers multiplied together 30 6 5

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**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

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**Prime The only factors of the integer are itself and one.**

EX: *1 EX: * 1

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**Composite There are many factors for the integer.**

EX: *24; 2*12; 3*8; 4*6 EX: *32; 2*16; 4*8

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**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

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**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

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**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

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**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

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**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

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Prime Factorization The list of prime factors in numerical order as products of each other.

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**Find the prime factorization of 81**

Draw two “branches” off of the number. 81

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**Find the prime factorization of 81**

Write two numbers that are factors of 81. 81 9

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**Find the prime factorization of 81**

Determine if the first number is prime or composite. 81 9 9

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**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

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**Find the prime factorization of 81**

The number 3 is prime, circle the numbers. 81 9 9 3 3

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**Find the prime factorization of 81**

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

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**Find the prime factorization of 81**

Now that all numbers are prime, write the prime factorization. 3 * 3 * 3 * 3 or 34 81 9 3

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**Find the prime factorization.**

34 75 28 120 225 16

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EXAMPLE 2 Identifying Prime and Composite Numbers

EXAMPLE 2 Identifying Prime and Composite Numbers

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