Divisibility tests

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

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.

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

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

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

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

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.

BY 4
(A)63204
(B)5521
(C)95344
(D)25306
(E)13258

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.

BY 5
(A)1302
(B)2205
(C)5500
(D)35506
(E)45891

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

BY 6
(A)55632
(B)15689
(C)2358
(D)98342
(E)11534

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
 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.
8

BY 8
(A)55130
(B)79120
(C)56048
(D)99864
(E)45408

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
e.g. : 15795
Here given number is 15795.
1+5+7+9+5 = 27 which is divisible by 9, hence the
9

BY 9
(A)65991
(B)55188
(C)78422
(D)150098
(E)250647

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
e.g. : 25600
Here the last digit is 0 hence 25600 is
divisible by 10.
10

BY 10
(A)63250
(B)5006
(C)98350
(D)45678
(E)6565

 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

BY 11
(A)5568947
(B)20051
(C)35642158
(D)2569
(E)1221

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

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