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Divisibility Rules and Factors

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In fifth grade, students need to be able to find factors of numbers. The information on the following slides might be helpful to parents and students who want to review important number ideas.

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Factors are numbers that can be multiplied together to get a product. For instance, 5 and 3 are factors of 15 because 5 x 3 = 15. 1 and 15 are also factors of 15 because 1 x 15 = 15.

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By fifth grade, we hope that students know their multiplication and division facts well enough that it is easy for them to recall the factors of many numbers. For instance, fifth grade students should know off the top of their heads that the factors of 27 are 1, 3, 9, and 27 because those are basic facts.

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However, when dealing with larger numbers that are not basic facts, knowing divisibility rules will help a student find factors. For instance, what are all the factors of 85?

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Knowledge of the basic facts will not reveal all the factors of 85. However, most students know that 5 is a factor of 85 because there is a 5 in the one’s place. Since 5 is a factor, we can find the related factor by dividing 85 by 5, which is 17. Knowing that 5 is a factor of a number that has a 5 in the one’s place is one of the divisibility rules all fifth grade students need to know.

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There are 7 divisibility rules that fifth grade students need to memorize and be able to use. Knowing them will help them find the factors of larger numbers. The divisibility rules are listed on the next slide.

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Divisibility Rules A number is divisible by: 2: if there is a 0, 2, 4, 6, or 8 in one’s place. 3: if the sum of the digits in the number is a multiple of 3. 4: if the number formed by the last two digits is a multiple of 4. 5: if there is a 0 or 5 in one’s place. 6: if the number is divisible by both 2 and 3. 9: if the sum of the digits in the number is a multiple of 9. 10: if there is a 0 in one’s place.

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Using divisibility rules will help a student find factors of larger numbers. For instance, a student might want to find all the factors of the number 114. Is 114 divisible by 2? Yes, because there is a 4 in the one’s place. Because the number is divisible by 2, we can find the related factor by dividing 114 by 2, which is 57. Is 114 divisible by 3? Yes, because the sum of all the digits (1 + 1 + 4) is 6, and 6 is a multiple of 3. Because the number is divisible by 3, we can find the related factor by dividing 114 by 3, which is 38. Is 114 divisible by 4? No, because the number formed by the ten’s digit and the one’s digit is 14, and 14 is not a multiple of 4. So far, we know some of the factors of 114. They are 2 x 57 3 x 38 And of course, 1 x 114. But, are there more? See the next slide to answer that question!

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114 Is 114 divisible by 5? No, because there is not a 0 or 5 in one’s place. Is 114 divisible by 6? Yes, because the number is divisible by both 2 and 3. Because the number is divisible by 6, we can find the related factor by dividing 114 by 6, which is 19. Is 114 divisible by 9? No, because the sum of the digits (1 + 1 + 4) is 6 and 6 is not a multiple of 9. Is 114 divisible by 10? No, because there is not a 0 in one’s place. We used all the divisibility rules and found the following factors of 114– 1 x 1142 x 573 x 386 x 19 WOW!!

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Remember, the whole reason to use divisibility rules is to help you find factors of larger numbers, which will be important in math work you do later on.

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We hope that this short Powerpoint presentation has been helpful to you in reviewing some of the ideas we have talked about in class. But we know you may still have questions. In addition to seeing your teacher, you can also get more help by visiting some of the web sites that we have links to on our Fifth Grade math web site. You can also see our fifth grade math super helper, Mrs. Bruder, at lunch recess.

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Thank you!

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