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.

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.

19. THANK YOU
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@reylkastro2
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