SPEED DIVISIBILITY TEST
How to quickly find if a number is divisible by another number. These are a few simple tests that can help you determine the divisibility of a number.
Important Rules: A number is (divisible by) –
- divisible by 2 if its last digit is even i.e. 0,2,4,6,8.
e.g. 370, 92, 2134, 686, 518 are divisible by 2 (you may verify!)
- divisible by 3 if the sum of its digits is divisible by 3.
e.g. 4365 is divisible by 3 since sum of its digits 4+3+6+5 = 18 is divisible by 3
- divisible by 4 if its last two digits (taken as a number) is divisible by 4.
e.g. 7936 is divisible by 4 since 36 is divisible by 4
- divisible by 5 if its last digit is 0 or 5.
e.g. both 2345 and 760 are divisible by 5
- divisible by 6 if its last digit is even and the sum of its digits is divisible by 3.
e.g. 7242 is divisible by 6 since last digit (2) is even and sum of the digits
7+2+4+2=15 is divisible 3
- for checking divisibility by 7, perform following steps-
- pick up the last digit and multiply it by 2
- then subtract this from the truncated original number
- check if this value is divisible by 7
- alternately continue doing this (steps i & ii) until you get single digit.
- if in step iii) answer is yes or in step iv) answer is 0 or ±7, then the given number is divisible by 7
e.g let us check for 686 . 68 – 2×6 = 56 which is divisible by 7 hence 686 is divisible by 7 (you may verify!)
- divisible by 8 if its last three digits (taken as a number) is divisible by 8.
e.g let us check for 31528 . 528/8 = 66. hence 31528 is divisible by 8(you may verify!)
- divisible by 9 if the sum of its digits is divisible by 9.
e.g. 6435 is divisible by 9 since sum of its digits 6+4+3+5 = 18 is divisible by 9
- divisible by 10 if its last digit is 0 .
e.g. 2760 is divisible by 10 (too obvious!)
- for checking divisibility by 11, perform following steps-
- find the sum of its digits at odd places
- find the sum of its digits at even places
- find the difference between two sums found at i) & ii)
- If the difference is 0 or divisible by 11, then the given number is divisible by 11
e.g let us check for 3841728 .
(sum of digits at odd places) – (sum of digits at even places)
= (3+4+7+8) – (8+1+2) = 11 which is divisible by 11. Hence the given number is divisible by 11
Using this guide you can quickly find if a number is divisible by another!