Number system - Divisiblity Test

Tests of divisibility - 

Divisibility by 2: A number is divisible by 2 if its unit digit is zero or an

even number.

Example: 248, 130

Divisibility by 3: A number is divisible by 3 if the sum of its digit is

divisible by 3.

Example: 273 ® 2 + 7 + 3 = 12.

12 is divisible by 3, hence 273 is divisible by 3.

Divisibility by 4: A number is divisible by 4 if the number formed by

its last two digits is divisible by 4.

Example: 236784

Here, 84 is divisible by 4, hence 236784 is divisible by 4.

Divisibility by 5: A number is divisible by 5 if the number or its unit digit is either 5 or 0.

Example: 115, 240, etc.

Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.

Example: 318, 396, etc.

Divisibility by 8: A number is divisible by 8 if the number formed by its last 3 digit is divisible by 8.

Example: 23816.

Here, 816 is divisible by 8, hence 23816 is divisible by 8.

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

Example: 72936 ® 7 + 2 + 9 + 3 + 6 = 27

27 is divisible by 9, hence 72936 is divisible by 9.

Divisibility by 11:A number is divisible by 11 if the difference of the

sum of the alternate digits starting from the units digit

and the sum of the alternate digits starting from the tens digit is either ‘0’ or is a multiple of 11.

Example: 1 3 3 1

(1 + 3) – (3 + 1) = 0 Þ 1331 is divisible by 11.

Divisibility by 19:A number is divisible by 19 if the sum of the number

formed by digits other than the unit digit and twice

the unit digit is divisible by 19.

Example: 76 Þ 7 + (2 × 6) = 19.

Therefore 76 is divisible by 19.