This document discusses divisibility rules for determining if a number is divisible by certain integers. It provides rules for divisibility by 2, 5, 10, 3, 6, 9, 4, 8, 12, and 11. For each rule, it gives an explanation of the concept and examples to demonstrate how to apply the rule. Readers are prompted to try applying the rules to various numbers to check for divisibility.

1. DIVISIBILTY

2. WHAT IS DIVISIBILITY?
It means if you divide one
number by another, the result is
a whole number WITHOUT a
remainder.
EXAMPLES:
12 ÷ 6 = 2 No remainder
15 ÷ 5 = 3 No Remainder

3. DIVISIBILITY RULE:
If the number is even, that is,
the number ends with 0, 2, 4, 6,
or 8, then the number is
divisible by 2.
28 46 912 354 2960
They are all divisible by 2.

4. DIVISIBILITY RULE:
If a number ends with 0 or
5, then the number is
divisible by 5.
600 805 2630 235
They are all divisible by 5 because their last digits
are either 0 or 5.

5. DIVISIBILITY RULE:
If the ones digit of a
number is zero, then the
number is divisible by 10.
600 890 2120 130
They are all divisible by 10 because their last digits
are 0.

6. DO THIS IN YOUR
NOTEBOOK!

7. Complete the chart. Write D on the appropriate space if the given
number is divisible by the number in the top row, or N if it is not.
2 5 10
92 640 D D D
45 835 N D N
92 724 D N N
45 678 D N N
94 136 D N N
245 648 D N N
802 185 N D N
914 000 D D D
48 360 472 D N N
65 927 640 D D D

8. DIVISIBILITY RULE:
To determine if a number is
divisible by 3, add the digits of
the number. If the sum of the
digits is divisible by 3, then the
number is divisible by 3.
Example: 6 312
6 + 3 + 1 + 2 = 12
12 divided by 3 is 4, so 6312 is divisible by 3.

9. Example: 27 531
2 + 7 + 5+3+1 = 18
18 divided by 3 is 6, so 27 531 is divisible by 3.
LETS HAVE A TRY !
Is 4284 divisible by 3?
Is 2293 divisible by 3?
Is 7689 divisible by 3?
Is 7726 divisible by 3?
YES
NO
YES
NO

10. Identify the numbers
divisible by 3.
Yes or No
1.562
2. 444
3. 432
4. 491
5. 127
NO
YES
YES
NO
NO

11. DIVISIBILITY RULE:
A number is divisible by 6 if it is
even and the sum of the digits is
divisible by 3. In short, the
number must be divisible by
both 2 and 3.
Example: 234 780
 The number 234,780 is an even number.
 2+3+4+7+8+0 = 24 (24 is divisible by 3)

12. LETS HAVE A TRY !
Is 25270 divisible by 6?
Is 26476 divisible by 6?
Is 44412 divisible by 6?
Is 56412 divisible by 6?
YES
NO
NO
YES

13. Identify the numbers
divisible by 6.
Yes or No
1.773
2. 816
3. 945
4. 162
5. 336
NO
YES
NO
YES
YES

14. DIVISIBILITY RULE:
A number is divisible by 9 if the
sum of its digits is a multiple of
9.
Example: 162
 1 + 6 + 2 = 9 (9 is in the multiplication table
of 9)
 Therefore 162 is divisible by 9.

15. LETS HAVE A TRY !
Is 12 917 divisible by 9?
Is 18315 divisible by 9?
Is 39918 divisible by 9?
Is 42619 divisible by 9?
NO
YES
NO
NO

16. Yes or No
1.342
2. 904
3. 201
4. 621
5. 225
Identify the numbers
divisible by 9.
YES
NO
NO
YES
YES

17. DIVISIBILITY RULE:
A number is divisible by 4 if the
number formed by its last two
digits is divisible by 4 or if the
last two digits are zeros.
Example: 216
 The last two digits which is 16 is divisible by
4.

18. LETS HAVE A TRY !
Is 95 632 divisible by 4?
Is 672 divisible by 4?
Is 9918 divisible by 4?
Is 1600 divisible by 4?
YES
YES
NO
YES

19. DIVISIBILITY RULE:
A number is divisible by 8 if the
number formed by its last three
digits is divisible by 8, or if the
last three digits are zeros.
Example: 7 136
 The last three digits which is 136 is divisible
by 8, then 7136 is divisible by 8.

20. LETS HAVE A TRY !
Is 19 640 divisible by 8?
Is 9 312 divisible by 8?
Is 464 divisible by 8?
Is 18 000 divisible by 8?
YES
YES
YES
YES

21. DIVISIBILITY RULE:
A number is divisible by 12 if the sum
of the digits is a multiple of 3 and the
last two digits are zeros or form a
number that is a multiple of 4.In short a
number is divisible by 12 if it is
divisible by both 3 and 4.
Example: 3 936
 3+9+3+6 = 21, which is divisible by 3
 36, which is divisible by 4
 So the number 3936 is divisible by 12

22. LETS HAVE A TRY !
Is 375 divisible by 12?
Is 729 divisible by 12?
Is 432 divisible by 12?
Is 756 divisible by 12?
NO
NO
YES
YES

23. DIVISIBILITY RULE:
STEP 1: Add the odd- positioned digits
starting from the left.
Ex. 40 634  4+6+4 =14
STEP 2: Add the even- positioned digits
starting from the left.
Ex. 40 634  3 +0= 3
STEP 3: Subtract the sums in this manner:
the greater sum minus the lesser sum.
Ex. 14 – 3 = 11

24. If the difference is 0 or multiple of 11,
then the given numbers is divisible by
11.
10 813  3 + 8 + 1= 12
Ex. 10 813
10 813  1 + 0 = 1
12 – 1 = 11
YES

25. LETS HAVE A TRY !
Is 495 divisible by 11?
Is 9835 divisible by 11?
Is 14 806 divisible by 11?
Is 918 291 divisible by 11?
YES
NO
YES
YES