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# Ch. 4, Sec 1: Divisability and Factors

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Chapter 4, Section 1 Notes on Divisibility Rules and Factors

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### Ch. 4, Sec 1: Divisability and Factors

1. 1. Chapter 4: Section 1: Divisibility and Factors By Ms. Dewey-Hoffman December 1 st , 2009
2. 2. Warm Ups for Chapter 4 <ul><li>Find the Quotient: 147  3 = </li></ul><ul><li>Find the Quotient: 273/3 = </li></ul><ul><li>Find the Quotient: 450/10 = </li></ul><ul><li>Find the Product: 4 • 4 • 4 = </li></ul><ul><li>Find the Product: (-2)(-2)(-2) = </li></ul><ul><li>Find the Product: (10)(10)(10)(10) = </li></ul>
3. 3. Warm Ups for Chapter 4 <ul><li>Write TWO numbers, that when multiplied together, give this product: </li></ul><ul><li>12 </li></ul><ul><li>50 </li></ul><ul><li>36 </li></ul><ul><li>24 </li></ul>
4. 4. Section 4.1: Divisibility and Factors <ul><li>One integer is DIVISIBLE by another if the remainder is 0 when you divide. </li></ul><ul><li>Divisibility Rules for 2, 5, and 10 . </li></ul><ul><li>An integer is divisible by… </li></ul><ul><li>2, if it ends in 0, 2, 4, 6, and 8 . </li></ul><ul><li>5, if it ends in 0 or 5 . </li></ul><ul><li>10, if it ends in 0 . </li></ul>
5. 5. Examples: Divisibility Rules <ul><li>Is the first number divisible by the second? </li></ul><ul><li>567 and 2? </li></ul><ul><li>1,015 and 5? </li></ul><ul><li>111,120 and 10? </li></ul><ul><li>53 and 2? </li></ul><ul><li>1,118 and 2? </li></ul>
6. 6. Divisibility Rule for 3 and 9. <ul><li>See if you can pick out the pattern… </li></ul>Yes Yes Yes Yes 1 + 0 + 1 + 7 = 9 1,017 No No No No 2 + 1 + 5 = 8 215 Yes Yes Yes Yes 4 + 6 + 8 = 18 468 No Yes No Yes 2 + 8 + 2 = 12 282 Is the Number Divisible by: 3? 9? Is the Sum Divisible by: 3? 9? Sum of Digits Number
7. 7. Divisibility Rule for 3 and 9. <ul><li>From the pattern we saw before… </li></ul><ul><li>An integer is divisible by… </li></ul><ul><li>3, if the sum of its digits is divisible by 3 . </li></ul><ul><li>9, if the sum of its digits is divisible by 9 . </li></ul>
8. 8. Example Problems: <ul><li>Is the first number divisible by the second? Explain. </li></ul><ul><li>64 by 9? </li></ul><ul><li>472 by 3? </li></ul><ul><li>174 by 3? </li></ul><ul><li>43,542 by 9? </li></ul>
9. 9. Finding Factors <ul><li>One integer is a FACTOR of another integer if it divides that integer with remainder zero. </li></ul>number number number
10. 10. Finding Factors <ul><li>So find all the different combinations of factors </li></ul><ul><li>12? </li></ul><ul><li>16? </li></ul><ul><li>18? </li></ul><ul><li>24? </li></ul>1(12), 2(6), 3(4): so, 1, 2, 3, 4, 6, and 12 1(16), 2(8), 4(4): so, 1, 2, 4, 8, and 16 1(18), 2(9), 3(6): so, 1, 2, 3, 6, 9, and 18 1(24), 2(12), 3(8), 4(6): so, 1, 2, 3, 4, 6, 8, 12, and 24
11. 11. Word Problem: <ul><li>There are 20 choral students singing at a school concert. Each row of singers much have the same number of students. If there are at least 5 students in each row, what are all the possible arrangements? </li></ul>
12. 12. List the positive factors of each number. <ul><li>10 </li></ul><ul><li>21 </li></ul><ul><li>31 </li></ul>1, 2, 5, 10 1, 3, 7, 21 1, 31
13. 13. Homework #40 <ul><li>USE YOUR NOTES TO REMIND YOU OF THE DIVISIBILITY RULES!!! </li></ul><ul><li>Page 174: 6-35 all. </li></ul>