This document provides an overview of divisibility tests for numbers 2 through 11. It explains the tests to check divisibility by each number without performing long division. For each number, it gives the method, such as checking the last digit for 2 and 5, summing the digits for 3 and 9, checking the last two digits for 4, last three digits for 8, separating odd and even digits for 11. It includes examples and practice problems checking divisibility for various numbers.

1. DIVISIBILITY
TESTS
BY:- Dr. VIVEK NAITHANI
T.G.T MATHS (K. V. S)
Copyright Information: CC by SA 4.0

2. WHAT IS A DIVISIBILITY TEST?
A divisibility test is a method to determine whether a given number is
divisible by certain number or not without actually dividing.
e. g. : 12 is divisible by 2, 3,4,6 and 12
Now to check this we generally divide 12 by any of these numbers and if
the remainder is 0 then we say that 12 is divisible by these numbers.
Now to avoid this long method we use divisibility tests to verify divisibility
without actually dividing.

3. To check whether the given number is divisible by 2
we have to see the digit at units place (last digit). If the
last digit (digit at units place) is even i. e. 0,2,4,6 or 8
then the complete number is divisible by 2.
 e.g. : 2514.
Here the given number is 2514. The last digit (digit at
units place) is 4 which is even. Hence the number 2514
is divisible by 4.
DIVISIBILITY TEST OF 2

4. CHECK THE DIVISIBILITY OF FOLLOWING
NUMBERS BY 2
(A)2365
(B)5398
(C) 5548
(D)7736
(E)105648

5. To check the divisibility of a given number by 3, we add
all the digits of the given number. If the sum of all the
digits is divisible by 3 then the entire number is divisible
by 3.
 e.g. : 15648
Here given number is 15648
Adding the digits 1+5+6+4+8 = 24 which is divisible
by 3.
Hence the entire number is divisible by 3
DIVISIBILITY TEST OF 3

6. CHECK THE DIVISIBILITY
BY 3
(A)56045
(B)2564331
(C)5004
(D)135679
(E)2453

7. To check the divisibility of a given number by 4, we check
the number formed by last two digits (digits at ones and
tens place). If the number formed by last two digits is
divisible by 4 then the complete number is divisible by 4.
e.g. : 51324
Here the given number is 51324. The number formed by
last two digits is 24 which is divisible by 4. Hence the
complete number is divisible by 4.
DIVISIBILITY TEST OF 4

8. CHECK THE DIVISIBILITY
BY 4
(A)63204
(B)5521
(C)95344
(D)25306
(E)13258

9. To check the divisibility of a given number by 5 we need
to check the digit at one place (last digit) of the number.
If the digit at units place (last digit) is either 0 or 5 then
the complete number is divisible by 5.
 e.g. : 2305
Here the last digit (digit at units place) is 5 so this
number 2305 is also divisible by 5.
DIVISIBILITY TEST OF 5

10. CHECK THE DIVISIBILITY
BY 5
(A)1302
(B)2205
(C)5500
(D)35506
(E)45891

11. To check whether a given number is divisible by 6 we check the
divisibility of the given number by 2 and 3 both.
If the number is divisible by 2 and 3 both then it is divisible by 6
also.
e.g. : 3568
Here the given number is 3568. The digit at ones place (last digit) is
8 which is even, so the given number is divisible by 2.
Now which is not divisible by 3.
Hence 3+5+6+8 = 22 the given number is not divisible by 6 as it is
not divisible by 2 and 3 both.
DIVISIBILITY TEST OF
6

12. CHECK THE DIVISIBILITY
BY 6
(A)55632
(B)15689
(C)2358
(D)98342
(E)11534

13. To check whether the given number is divisible by eight we
check the number formed by last three digits (digits at ones,
tens and hundreds place).
If the number formed by last three digits is divisible by 8 then
the complete number is divisible by 8.
 e.g. : 9723024
Here the given number is 9723024. The number formed by last
3 digits is 024 which is divisible by 8. Hence the complete
number is divisible by 8.
DIVISIBILITY TEST OF
8

14. CHECK THE DIVISIBILITY
BY 8
(A)55130
(B)79120
(C)56048
(D)99864
(E)45408

15. To check whether the given number is divisible by 9 we
add all the digits of the given number.
If the sum of the digits is divisible by 9 then the
complete number is divisible by 9.
e.g. : 15795
Here given number is 15795.
1+5+7+9+5 = 27 which is divisible by 9, hence the
complete number is divisible by 9.
DIVISIBILITY TEST OF
9

16. CHECK THE DIVISIBILITY
BY 9
(A)65991
(B)55188
(C)78422
(D)150098
(E)250647

17. To check whether the given number is
divisible by 10, we check the last digit (digit
at ones place).
If the digit at ones place (last digit) is 0 then
the complete number is divisible by 10.
e.g. : 25600
Here the last digit is 0 hence 25600 is
divisible by 10.
DIVISIBILITY TEST OF
10

18. CHECK THE DIVISIBILITY
BY 10
(A)63250
(B)5006
(C)98350
(D)45678
(E)6565

19. DIVISIBILITY TEST OF 11
 To check whether the given number is divisible by 11 we follow the following steps:
 We first separate the digits at odd places and digits at even places and add them separately.
 Then we subtract the sum of digits at even places and sum of digits at odd places.
 If the difference is 0 or a multiple of 11 then the given number is divisible by 11.
 e.g.: 15698725
 Sum of digits at even places = 1+4+8+2 = 15
 Sum of digits at odd places = 5+9+7+5 = 26
 Difference = 26-15 = 11. Hence the given number is divisible by 11.
 The number is divisible by 11 when difference is 0, 11, 22, 33, … etc. i.e. multiple of 11
Place Even Odd Even Odd Even Odd Even Odd
Digit 1 5 4 9 8 7 2 5

20. CHECK THE DIVISIBILITY
BY 11
(A)5568947
(B)20051
(C)35642158
(D)2569
(E)1221

21. CHECK THE DIVISIBILITY OF
FOLLOWING NUMBERS
Find by which numbers from 2 to 11 the following numbers are
divisible
(A)6598
(B)55671
(C)15124
(D)21647
(E)32315

22. THANK
YOU