Divisibility
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This document discusses divisibility rules for determining if a number is divisible by certain divisors without performing long division. It provides rules for testing if a number is divisible by divisors from 1 to 16 by examining the numbers digits. For example, a number is divisible by 2 if its last digit is even, divisible by 5 if its last digit is 0 or 5, and divisible by 3 if the sum of its digits is divisible by 3. Examples are given to demonstrate how to apply these tests to determine divisibility.
Divisibility
- 1. Divisibility www.slideshare.net/reycastro1 The Nature of Modern Mathematics
- 2. Divisibility A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits. Wikipedia
- 3. Every number M is divisible by 1. 1|a. this is true, since we will always find a number k so that 𝒂 = 𝟏 ∙ 𝒌. like: a. 23 b. 41 DIVISIBILITY BY 1
- 4. If the last digit of the number is even, then the number is divisible by 2. ( 0, 2, 4, 6, or 8) Like: 341, 592 DIVISIBILITY BY 2
- 5. If the number made up of the last two digits of a number M, is divisible by 4, then the number is also divisible by 4. Like: 341, 592 DIVISIBILITY BY 4
- 6. If the number made up of the last three digits of a number M, is divisible by 8, then the number is also divisible by 8. Like: 341, 592 DIVISIBILITY BY 8
- 7. If the number made up of the last four digits of a number M, is divisible by 16, then the number is also divisible by 16. Like: 341, 592 DIVISIBILITY BY 16
- 8. If the last digit of a number M, is 0 or 5, then M is divisible by 5. Like: 341, 592 DIVISIBILITY BY 5
- 9. If the last digit of a number M, is 0, then M is divisible by 10. Like: 341, 592 DIVISIBILITY BY 10
- 10. If the sum of the digits is divisible by 3. Like: 341, 592 DIVISIBILITY BY 3
- 11. If it is divisible by 2 and by 3. Like: 341, 592 DIVISIBILITY BY 6
- 12. f the sum of the digits is divisible by 9. Like: 341, 592 DIVISIBILITY BY 9
- 13. Take all the digits except the last three digits, then subtract all the digits to the last three digits. Ex. a) 139, 125; by 7 b) 12,478,375; by 13 c) 57,945,822; by 11 Divisibility by 7, by 11, and by 13.
- 14. If it is divisible by 2 and by 7. Like: 341, 592 DIVISIBILITY BY 14
- 15. If it is divisible by 3 and by 5. Like: 2,931,930 DIVISIBILITY BY 15
- 16. If it is divisible by 3 and by 4. Like: 341, 592 DIVISIBILITY BY 12
- 17. Example of divisibility › Consider each number 1 through 16, and tell whether it will divide evenly into 3,257, 618. › Exercises: A. Tell if it is true. 1) 8|136, 2) 15|4814 3) 17|255 B. Test the number for divisibility by each number 1 through 16. 4) 82, 258 5) 720, 720
- 18. Sources: • Wikipedia • Shortcut To Divisibility By 7, 11, 13, Score More Aptitude English, Youtube Channel, 2015. • Smith Karl J., The Nature of Modern Mathematics, Brooks/Cole Publishing Co. California, 1973.