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Prime Factorization 7 th Grade Math

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Prime Factorization Of a Number A prime number is a counting number that only has two factors, itself and one. Counting numbers which have more than two factors (such as six, whose factors are 1, 2, 3 and 6), are said to be composite numbers. When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number. There are several different methods that can be utilized for the prime factorization of a number.

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Using Division Prime factors can be found using division. Keep dividing until you have all prime numbers. The prime factors of 78 are 2, 3, 13.

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Remember the Divisibility Rules IIIIf the last digit is even, the number is divisible by 2. IIIIf the last digit is a 5 or a 0, the number is divisible by 5. IIIIf the number ends in 0, it is divisible by 10. IIIIf the sum of the digits is divisible by 3, the number is also. IIIIf the last two digits form a number divisible by 4, the number is also.

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More divisibility rules… IIIIf the number is divisible by both 3 and 2, it is also divisible by 6. TTTTake the last digit, double it, and subtract it from the rest of the number; if the answer is divisible by 7 (including 0), then the number is also. IIIIf the last three digits form a number divisible by 8, then the whole number is also divisible by 8. IIIIf the sum of the digits is divisible by 9, the number is also.

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Using the Factor Tree 78 78 / \ / \ 2 x 39 2 x 39 / / \ / / \ 2 x 3 x 13

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Exponents 72 72 / \ / \ 8 x 9 8 x 9 / \ / \ / \ / \ 2 x 4 x 3 x 3 2 x 4 x 3 x 3 / / \ \ \ / / \ \ \ 2 x 2 x 2 x 3 x 3 2 x 2 x 2 x 3 x 3 Another key idea in writing the prime factorization of a number is an understanding of exponents. An exponent tells how many times the base is used as a factor. 72 = 2 3 x 3 2

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Let’s Try a Factor Tree! 84 84 / \ / \ 2 x 42 2 x 42 / / \ / / \ 2 x 2 x 21 2 x 2 x 21 / / / \ / / / \ 2 x 2 3 x 7 2 x 2 3 x 7 What is the final factorization? 2 2 x 3 x 7 = 84

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Factor Trees do not look the same for the same number, but the final answer is the same. 72 72 / \ / \ 8 x 9 8 x 9 / \ / \ / \ / \ 2 x 4 x 3 x 3 2 x 4 x 3 x 3 / \ / \ 2 x 2 x 2 x 3 x 3 2 x 2 x 2 x 3 x 372 / \ / \ 2 x 36 2 x 36 / / \ / / \ 2 x 2 x 18 2 x 2 x 18 / / / \ / / / \ 2 x 2 x 2 x 9 2 x 2 x 2 x 9 / / / / \ / / / / \ 2 x 2 x 2 x 3 x 3 2 x 2 x 2 x 3 x 3

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Greatest Common Factors One method to find greatest common factors is to list the factors of each number. The largest number is the greatest common factor. Let’s find the factors of 72 and 84. 72 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 84 1, 2, 3, 4, 6, 12, 14, 21, 28, 42, 84

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Prime Factorization is helpful for finding greatest common factors. 72 72 / \ / \ 8 x 9 8 x 9 / \ / \ / \ / \ 2 x 4 x 3 x 3 2 x 4 x 3 x 3 / \ / \ 2 x 2 x 2 x 3 x 3 2 x 2 x 2 x 3 x 3 Take the common prime factors of each number and multiply to find the greatest common factor. 84 84 / \ / \ 2 x 42 2 x 42 / / \ / / \ 2 x 2 x 21 2 x 2 x 21 / / / \ / / / \ 2 x 2 3 x 7 2 x 2 3 x 7 2 x 2 x 3 = 12

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Resources IXL.Com – Sixth Grade – N.5 Prime Factorization Please log on when you access the webpage below: http://www.ixl.com/math/grade- 6/prime-factorization http://www.ixl.com/math/grade- 6/prime-factorization

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