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## Prime Factorization

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**Prime Factorization**Factor Trees**30**Find the prime factorization of 30 • Draw two “branches” off of the number.**30**6 5 Find the prime factorization of 30 • Write two numbers that are factors of 30. *Remember: factors are the numbers multiplied together**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.**81**Find the prime factorization of 81 • Draw two “branches” off of the number.**81**9 9 Find the prime factorization of 81 • Write two numbers that are factors of 81.**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**81**9 9 3 3 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**Find the prime factorization.**• 34 • 75 • 28 • 120 • 225 • 16