A small Divisibility Trick for any number

Sometimes it becomes very cumbersome to check the divisibility by the conventional methods specially in case of 7, 11, 13…. etc.

Since the divisibility methods corresponding to these numbers takes good amount of time, we mostly tend to divide the number simply by these numbers. Even if you are able to apply these methods, remembering these methods is a quite tough task.

So why don’t we go with a simple trick to solve the problem faster.

The method which I am going to talk about would deal with the number simply by DIVISION, but you can do it in your mind. Though this method would be effective for smaller numbers.

So Lets try to check the divisibility of a number 4564 by 7.

Step 1: Try to find a ‘simple’ multiple of 7 close to 4564.

what comes to your mind first. is it 4200?? isn’t it 🙂

Step 2: Distribute the number in addition form

4567 = 4200 + 364

Step 3: Repeat the process until you get those few digits which is easily recognizable in terms of divisibility.

4564 = 4200 + 3674= 4200 + 350 + 14.

So we can clearly say 4564 is divisible by 7.

One more advantage in this method is along-with checking of divisibility you directly get the quotient and remainder.

4564 = 4200 + 350 + 14 = 7 x (600+50+2) = 7 x (652)

quotient = 652 , remainder = 0.