Online CAT Lessons:-
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Divisibility Checks for various digits.
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Its always advantageous to know the divisibility rules of various digits so that we can save a lot of time during our calculations and its extremely useful for elimination of answer choices.
In an exam like CAT or GMAT, the most important thing is not to arrive at the answer, but arrive at the answer fast if possible, without doing any calculation you will have to find the answer. So,when you get an objective type question,uy first aim should be to eliminate at least 2 options. The knowledge in rules like divisibility, factors etc will come handy there.

The basic rule in finding the divisibility of a number is that we should find a power of 10(if we r using decimal system) which is completely divisible by the specific digit.
Or we need to find the power which gives a rem. of +/-1.

Divisibility Checks for 2
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We know that rem (10/2)=0.
ie rem(10^1/2) = 0.So we need to check the last digit of a no. only for checking its divisibility by 2.
****The last digit should be 2,4,6,8 or 0.****

Divisibility Checks for 3
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We can write any no. in decimal abc in the form 100a+10b+c
Again, abc = 99a+9b+(a+b+c)

Here except the last term,all terms are divisibe by 9 hence also by 3
Hence if the term ( a+b+c) which is the digit sum of the no. is divisible by 3,the no.abc is divisible by 3.

****The digit sum of a no. should be a multiple of 3****

Divisibility Checks for 4
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We know that rem (10^2/4)=0.
So we need to check the last 2 digits of a no. for checking its divisibility by 4.

****The last 2 digits should be divisible by 4.****

Divisibility Checks for 5
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The last digit should be 5 or 0.

****The last digit should be divisible by 5 or 0.****


Divisibility Checks for 6
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6=2*3.
A no. is divisible by 6,if its divisible by both 2 &3.

****The no. should be divisible by both 2 &3****

Divisibility Checks for 7
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We know that rem (10^3/7)=-1.
therefore rem(10^6/7) = +1.
So if we need to check the divisibility of a 6 digit number 'abcdef'
we need to split the number in to 2, 'abc' and 'def'
Now we need to take the difference between the two numbers and check whether its divisible by 7.If its divisible,then the large number is divisible by 7.

Divisibility Checks for 8
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We know that rem (10^3/8)=0.
So we need to check the last 3 digits of a no. for checking its divisibility by 8.

****The last 3 digits should be divisible by 8.****

Divisibility Checks for 9
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We can write any no. in decimal abc in the form 100a+10b+c
Again, abc = 99a+9b+(a+b+c)

Here except the last term,all terms are divisibe by 9.
Hence if the term ( a+b+c) which is the digit sum of the no. is 9,the no.abc is divisible by 9.

****The digit sum of a no. should be 9****

The divisibility check for higher prime numbers will be given in next lesson