Dear readers

**Chapter:-Test of Divisibility**

This chapter is necessary all whose preparation competition exam.i think this is help full for all candidates. Thanks to visiontoday team.for chapters visit regular www.visiontoday.in

More details below

**TESTS OF DIVISIBILITY**

There are certain tests of divisibility that can help us to decide whether a given number is divisible by another number.

1. **Divisibility of numbers by 2:**

► A number that has 0, 2, 4, 6 or 8 in its ones place is divisible by 2.

2. **Divisibility of numbers by 3**

► A number is divisible by 3 if the sum of its digits is divisible by 3.

3. **Divisibility of numbers by 4**

► A number is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.

4. **Divisibility of numbers by 5**

► A number that has either 0 or 5 in its ones place is divisible by 5.

5. Divisibility of numbers by 6:

► A number is divisible by 6 if that number is divisible by both 2 and 3.

6. **Divisibility of numbers by 7:**

► A number is divisible by 7, if the difference b/w twice the last digit and the no. formed by the other digits is either 0 or a multiple of 7. eg. 2975, it is observed that the last digit of 2975 is ‘5’, so, 297 –(5×2) = 297 – 10 =287, which is a multiple of 7 hence, it is divisible by 7

7. **Divisibility of numbers by 8:**

► A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

8. **Divisibility of numbers by 9:**

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

9. **Divisibility of numbers by 10:**

► A number that has 0 in its ones place is divisible by 10.

10. **Divisibility of numbers by 11:**

► If the difference between the sum of the digits at the odd and even places in a given number is either 0 or a multiple of 11, then the given

number is divisible by 11.

11. **Divisibility of number by 12.**

► Any number which is divisible by both 4 and 3, is also divisible by 12. To check the divisiblity by 12, we i. First divide the last two-digit number by 4. If it is not divisible by 4, it is divisible by 4 is not divisible by 12. If it is divisible by 4 them. ii. Check whether the number is divisible by 3 or not.

Ex: 135792 : 92 is divisible by 4 and also (1 + 3 + 5 + 7 + 9

+2 =) 27 is divisible by 3 ; hence the number is divisible

by 12.

12. **Divisibility by 13**

Oscillator for 13 is 4. But this time, our oscillator is not negative (as in case of 7) It is ‘one-more’ Oscillator. So, the working Principle will be different now.

Eg: Is 143 divisible by 13 ? Sol: 14 3 : 14 + 3 x 4 = 26

Since 26 is divisible by 13, the number 143 is also

divisible by 13. Eg 2 : Check the divisibility by 13. 2 416 7

26/6/20/34 [ 4 x 7 ( from 24167 ) + 6 ( from 24 167) =

34] [4 x 4 ( from 3 4 ) + 3 (from 3 4 ) + 1 (from 24167)]

=20 [4 x 0 (from 2 0 ) + 2 (from 20) + 4 (from 24 167)= 6]

[4 x 6 (from 6 ) + 2 (from 24 167)= 26] Since 26 is

divisible by 13 the number is also divisible by 13.

- 13..
**Divisibility by 14**

► Any Number which is divisible by both 2 and 7, in also

divisible by 14. That is, the number’s last digit should be

even and at the same time the number should be divisible

by 7.14.

**Divisibility by 15**

► Any number which is divisible by both 3 and 5 is also divisible by 15.

15. **Divisibility by 16**

► Any number whose last 4 digit number is divisible by

16 is also divisible by 16.

- 16.
**Divisibility by 17**

► Negative Oscillator for 17 is 5. The working for this is the same as in the case 7. Eg: check the divisibility of 1904 by 17

Sol: 1904 : 190 – 5 x 4 = 170 Since 170 is divisible by 17,

the given number is also divisible by 17. E.g 2: 957508 by

17

So1:95750 8: 95750 – 5 x 8 = 95710 9571 0 : 9571 – 5 x 0 = 9571 957 1 : 957 – 5 x 1 = 952 952 : 95 – 5×2 =85

Since 85 is divisible by 17, the given number is divisible by 17.

17.**Divisibility by 18**

► Any number which is a divisible by 9 has its last digit

(unit-digit) even or zero, is divisible by 18. Eg. 926568 :

Digit – Sum is a multiple of nine (i.e, divisible by 9) and

unit digit (8) is even, hence the number is divisible by 18.

18. **Divisibility by 19**

► If recall, the ‘one-more’ osculator for 19 is 2. The method is similar to that of 13, which is well known to us. Eg. 1 4 9 2 6 4 19/9/12/11/14

General rules of divisibility for all numbers:

♦ If a number is divisible by another number, then it is

also divisible by all the factors of the other number.

♦ If two numbers are divisible by another number, then

their sum and difference is also divisible by the other

number.

♦ If a number is divisible by two co-prime numbers, then it is also divisible by the product of the two co-prime numbers.

For latest update regular visit **www.visiontoday.in**

Thanks to readers any query or any give any suggestions. plese give ur feedback in comment box.