Ch. 4, Sec 1: Divisability and Factors
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This document provides instruction on divisibility rules and factors. It begins with warm up exercises on division and multiplication. It then covers divisibility rules for numbers 2, 5, 10, 3, and 9 based on the digits in the number. Examples are provided to demonstrate applying the rules. Factors of numbers are defined as integers that fully divide into that number. Examples of finding all the factors of various numbers are given. The document concludes with a word problem about arranging choral students in rows.
Ch. 4, Sec 1: Divisability and Factors
- 1. Chapter 4: Section 1: Divisibility and Factors By Ms. Dewey-Hoffman December 1 st , 2009
- 2. Warm Ups for Chapter 4 Find the Quotient: 147 3 = Find the Quotient: 273/3 = Find the Quotient: 450/10 = Find the Product: 4 • 4 • 4 = Find the Product: (-2)(-2)(-2) = Find the Product: (10)(10)(10)(10) =
- 3. Warm Ups for Chapter 4 Write TWO numbers, that when multiplied together, give this product: 12 50 36 24
- 4. Section 4.1: Divisibility and Factors One integer is DIVISIBLE by another if the remainder is 0 when you divide. Divisibility Rules for 2, 5, and 10 . An integer is divisible by… 2, if it ends in 0, 2, 4, 6, and 8 . 5, if it ends in 0 or 5 . 10, if it ends in 0 .
- 5. Examples: Divisibility Rules Is the first number divisible by the second? 567 and 2? 1,015 and 5? 111,120 and 10? 53 and 2? 1,118 and 2?
- 6. Divisibility Rule for 3 and 9. See if you can pick out the pattern… 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. Divisibility Rule for 3 and 9. From the pattern we saw before… An integer is divisible by… 3, if the sum of its digits is divisible by 3 . 9, if the sum of its digits is divisible by 9 .
- 8. Example Problems: Is the first number divisible by the second? Explain. 64 by 9? 472 by 3? 174 by 3? 43,542 by 9?
- 9. Finding Factors One integer is a FACTOR of another integer if it divides that integer with remainder zero. number number number
- 10. Finding Factors So find all the different combinations of factors 12? 16? 18? 24? 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. Word Problem: 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?
- 12. List the positive factors of each number. 10 21 31 1, 2, 5, 10 1, 3, 7, 21 1, 31
- 13. Homework #40 USE YOUR NOTES TO REMIND YOU OF THE DIVISIBILITY RULES!!! Page 174: 6-35 all.