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Prime Factorization Section 2.5

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Objectives Find the prime factorization of a counting number by repeated division Find the prime factorization of a counting method using the tree method

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Objective 1: Find the prime factorization of a counting number by repeated division

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Obj. 1: Repeated Division The basic elements of all numbers are the prime numbers Every counting number (except 1) is a prime or a combination of prime factors

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Obj. 1: Repeated Division To find the prime factorization of a counting number –Divide the counting number and each following quotient by a prime number until the quotient is 1. –Begin with 2 and divide until quotient is odd –Divide by 3 until quotient is not a multiple of 3 –Continue with 5, 7, and so on –Write answer as factors multiplied together –Can use exponents as shorthand

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Objectives2: Find the prime factorization of a counting method using the tree method

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Obj. 2: Tree Method To find the prime factorization using the tree method –Draw “factor branches” from the given number with any two factors –Draw additional branches from the factor at the end of the branch –Factoring is complete when numbers at end of each branch is a prime number –Write answer as factors multiplied together –Can use exponents as shorthand

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Searching for Factor Strings Some numbers can be written as the product of several different pairs of factors, like 24. It is also possible to write this.

Searching for Factor Strings Some numbers can be written as the product of several different pairs of factors, like 24. It is also possible to write this.

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