Test for divisibility of a Number Algebra, Quantitative Aptitude Test Study material for SSC, Tips in Numerical for Competitive Examinations

Testing divisibility of any number is really simple and easy. But if you don't know the simple trick on how to check the divisibility of a large digit number, you will definitely waste your precious time in your examination hall. For SSC, UPSC , PSC and other public examinations, all the questions will be simple so everyone can solve the question. But what matter is time. When you solve a quantitative aptitude question within one minute means you can solve 95% of questions within the given time limit. Here you will learn the divisibility of any numbers using numbers from 2 to 19 with simple calculations.

### All Quantitative Aptitude Topics can be Found Here

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**How to check the divisibility of a Number by 2**

If the last digit of a number is even or zero the number is divisible by 2**Eg:**Check whether 54876 is divisible by 2

**Solution :**The last digit of the number is "6", 6 is even so the number is divisible by 2

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**Divisibility of a number by 3**

If sum of all digits of a number is divisible by 3, the number will be divisible by 3**Eg :**Check Whether 35667 is divisible by 3

**Solution :**Sum of digits = 3+5+6+6+7 = 27

27 is divisible by 3, so the number 35667 is divisible by 3

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**Divisibility of a Number by 4**

If the last two digits of a number is divisible by 4, the number will be divisible by 4 or two zeros(00)**Eg :**Check whether 555364 is divisible by 4

**Solution :**the last two digit of the number is 64, which is divisible by 4

So the number 555364 is divisible by 4

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**Divisibility of a Number by 5**

If the last digit is "5" or "0" the number is divisible by five (5)
Eg: Check whether 12364795 is divisible by 5

Solution : The last digit is 5, so the number is divisible by 5

#### Divisibility of a number by 6

If the given number is divisible by both 2 and 3, the number will be divisible by 6
Eg: Check whether 32868 is divisible by 6

Solution : Last digit is 8, which is even. ie the number is divisible by 2

Sum of digits = 3+2+8+6+8 = 27, 27 is divisible by 3, so the number is divisible by 3

Since the number is divisible by both 2&3, the number is divisible by 6

#### Divisibility of a number by 7

Scroll down to the last section#### Divisibility of a number by 8

If the last three digits are divisible by 8 or three zeros (000), the number will be divisible by 8
Eg: Check whether 364200 is divisible by 8

Solution : Last three digit in this number is 200, which is divisible by 8. ie the number is divisible by 8

#### Divisibility of a number by 9

If the sum of the digits in the number is divisible by 9, the number will be divisible by 9
Eg: Check whether 292914 is divisible by 9

Solution : The sum of the digits in the number = 2+9+2+9+1+4 = 27, 27 is divisible by 9, ie the number is divisible by 9

#### Divisibility of a number by 10

If the last digit in the number is zero, the number is divisible by 10
Eg: 548712540

Solution : Last digit in this number is zero, ie the number is divisible by 10

#### Divisibility of a number by 11

If the some of the alternate digits in a number are equal, then the number is divisible by 11
Eg: Check whether 3245682 is divisible by 11

Solution : Sum of alternate digits

ie 3+4+6+2 = 15

2+5+8 = 15

sum of alternate digits are equal, ie the number is divisible by 11

#### Divisibility of a number by 12

#### Divisibility of a number by 7,13,17 and 19

We have skipped checking divisibility of a number using 7 above, because the method used for checking the divisibility of a number by 7,13 and 17 are almost same. The method falls into the same category.

For the numbers 7,13 and 17 we have to find osculator and negative osculator

**Osculator :**

Eg: To find the osculatot of 59, find the nearest multiple of 10 of that number. ie 60 (50+1)

60 can be written as 6x10, means 6 is the oscullaotot

If the number is 41 , nearest multiple of 10 is 40

4x10 and negative osculator is 4

- [message]
- Important
- The number you are adding or subtracting to get multiple of 10 should be +1 or -1

#### Divisibility of a number by 7

Find multiple of 7 more than 15, which is 21

Nearest multiple of 10 for 21 is 20 (21-1)

20 can be written as 2x10 and 7 is having negative osculator of 2 (-2)

nearest multiple of 10 is 40

40 can be written as 4x10 and oscullator is 4

Eg: Check whether 2009 is divisible by 7

Solution : 200 + (9*-2) [ here -2 is negative osculator]

200-18 = 182

Again for 182, 18+(2*-2) = 18-4 = 14, 14 is divisible by 7 so 2009 is divisible by 7

#### Divisibility of a number by 13

Finding osculator : 13*3 = 39nearest multiple of 10 is 40

40 can be written as 4x10 and oscullator is 4

Eg : Check whether 1573 is divisible by 13

Solution 1573 } 157+ (3*4) = 157+12 = 169, 169 is divisible by 13

or 169 } 16 + (9*4) = 16+36 = 52, 52 is divisible by 13

#### Divisibility of a number by 17

Finding osculator : 17*3 = 51

51 can be written as 51-1 = 50 } -5 is osculator

Eg : Check whether 1904 is divisible by 17

1904 } 190+ (4*-5) = 170, 170 is divisible by 17

or 170 } 17+ (0*-5) = 17, 17 is divisible by 17

### All Quantitative Aptitude Topics can be Found Here

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