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Maths Tricks for SSC CGL Exam 2016-2017  Mathematics shortcut Tricks with explanation for Competitive Exams follow our Online Test Series for all government Jobs and Banking Jobs. DivisibilityDivisible By 



One whole number is divisible by another if the remainder we get after the division is zero.
Examples
36 is divisible by 4 because 36 ÷ 4 = 9 with a remainder of 0.
36 is divisible by 6 because 36 ÷ 6 = 6 with a remainder of 0.
36 is not divisible by 5 because 36 ÷ 5 = 7 with a remainder of 1.
Divisibility Rules
By using divisibility rules, we can easily find whether a given number is divisible by another number without actually performing the division. This saves time especially when working with numbers. Divisibility rules of numbers 1 to 10 are provided below.
Divisibility Rule
Description
Examples
Divisibility by 2
A number is divisible by 2 if the last digit is even. i.e., if the last digit is 0 or 2 or 4 or 6 or 8

Example 1: Check if 64 is divisible by 2.
The last digit of 64 is 4 (even).
Hence 64 is divisible by 2


Example 2: Check if 69 is divisible by 2.
The last digit of 69 is 9 (not even).
Hence 69 is not divisible by 2

Divisibility by 3

A number is divisible by 3 if the sum of the digits is divisible by 3
Please note that we can apply this rule to the answer again and again if needed.

Example 1: Check if 387 is divisible by 3.
3 + 8 + 7 = 18.
18 is divisible by 3.
Hence 387 is divisible by 3


Example 2: Check if 421 is divisible by 3.
4 + 2 + 1 = 7.
7 is not divisible by 3.
Hence 421 is not divisible by 3

Divisibility by 4

A number is divisible by 4 if the number formed by the last two digits is divisible by 4.

Example 1: Check if 416 is divisible by 4.
Number formed by the last two digits = 16.
16 is divisible by 4.
Hence 416 is divisible by 4


Example 2: Check if 481 is divisible by 4.
Number formed by the last two digits = 81.
81 is not divisible by 4.
Hence 481 is not divisible by 4

Divisibility by 5

A number is divisible by 5 if the last digit is either 0 or 5.
Example 1: Check if 305 is divisible by 5.
Last digit is 5.
Hence 305 is divisible by 5.


Example 2: Check if 420 is divisible by 5.
Last digit is 0.
Hence 420 is divisible by 5.


Example 3: Check if 312 is divisible by 5.
Last digit is 2.
Hence 312 is not divisible by 5
Divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3
Example 1: Check if 546 is divisible by 6.
546 is divisible by 2.
546 is also divisible by 3. 
Hence 546 is divisible by 6


Example 2: Check if 633 is divisible by 6.
633 is not divisible by 2 though it is divisible by 3. 
Hence 633 is not divisible by 6


Example 3: Check if 635 is divisible by 6.
635 is not divisible by 2.
635 is also not divisible by 3.
Hence 635 is not divisible by 6


Example 4: Check if 428 is divisible by 6.
428 is divisible by 2 but it is not divisible by 3.
Hence 428 is not divisible by 6
Divisibility by 7

To find out if a number is divisible by 7, double the last digit and subtract it from the number formed by the remaining digits.


Repeat this process until we get at a smaller number whose divisibility we know.


If this smaller number is 0 or divisible by 7, the original number is also divisible by 7.

Example 1: Check if 349 is divisible by 7.
Given number = 349
34 - (9 × 2) = 34 - 18 = 16
16 is not divisible by 7.
Hence 349 is not divisible by 7


Example 2: Check if 364 is divisible by 7.
Given number = 364
36 - (4 × 2) = 36 - 8 = 28
28 is divisible by 7.
Hence 364 is also divisible by 7


Example 3: Check if 3374 is divisible by 7.
Given number = 3374
337 - (4 × 2) = 337 - 8 = 329
32 - (9 × 2) = 32 - 18 = 14
14 is divisible by 7.
Hence 329 is also divisible by 7.
Hence 3374 is also divisible by 7
Divisibility by 8
A number is divisible by 8 if the number formed by the last three digits is divisible by 8
Example 1: Check if 7624 is divisible by 8.
The number formed by the last three digits of 7624 = 624.
624 is divisible by 8.
Hence 7624 is also divisible by 8.


Example 2: Check if 129437464 is divisible by 8.
The number formed by the last three digits of 129437464 = 464.
464 is divisible by 8.
Hence 129437464 is also divisible by 8.


Example 3: Check if 737460 is divisible by 8.
The number formed by the last three digits of 737460 = 460.
460 is not divisible by 8.
Hence 737460 is also not divisible by 8
Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.


(Please note that we can apply this rule to the answer again and again if we need)

Example 1: Check if 367821 is divisible by 9
3 + 6 + 7 + 8 + 2 + 1 = 27
27 is divisible by 9.
Hence 367821 is also divisible by 9.


Example 2: Check if 47128 is divisible by 9
4 + 7 + 1 + 2 + 8 = 22
22 is not divisible by 9.
Hence 47128 is not divisible by 9.


Example 3: Check if 4975291989 is divisible by 9
4 + 9+ 7 + 5 + 2 + 9 + 1 + 9 + 8 + 9= 63
Since 63 is big, we can use the same method to see if it is divisible by 9.
6 + 3 = 9
9 is divisible by 9.
Hence 63 is also divisible by 9.
Hence 4975291989 is also divisible by 9
Divisibility by 10

A number is divisible by 10 if the last digit is 0.

Example 1:Check if 2570 is divisible by 10.
Last digit is 0.
Hence 2570 is divisible by 10.


Example 2: Check if 5462 is divisible by 10.
Last digit is not 0.
Hence 5462 is not divisible by 10



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