# DIVISIBILITY RULE FOR 4

Rule :

In a number, if the last two digits are zeroes or the number formed by the last 2 digits is divisible by 4, then the number is divisible by 4.

Problem 1 :

Which of these numbers are divisible by 4?

a) 482   b) 2556  c) 8762  d) 12368  e) 213 186

Solution :

a) 482

In the given number 482, the last two digits are not zeroes.

And also, the number formed by the last two digits is 82 which is not divisible by 4.

So, the given number 482 is not divisible by 4.

b) 2556

In the given number 2556, the last two digits are not zeroes.

But, the number formed by the last two digits is 56 which is divisible by 4.

So, the given number 2556 is divisible by 4.

c) 8762

In the given number 8762, the last two digits are not zeroes.

And also, the number formed by the last two digits is 62 which is not divisible by 4.

So, the given number 8762 is not divisible by 4.

d) 12368

In the given number 12368, the last two digits are not zeroes.

But, the number formed by the last two digits is 68 which is divisible by 4.

So, the given number 12368 is divisible by 4.

e) 213 186

In the given number 213 186, the last two digits are not zeroes.

And also, the number formed by the last two digits is 86 which is not divisible by 4.

So, the given number 213 186 is not divisible by 4.

Problem 2 :

If the product of 4864 x 9P2 is divisible by 12, the value of P is

a)  1     b)  5    c) 6      d) 8

Solution :

To check if the number is divisible by 12, it must be the multiple of 4 and 3.

In the given numbers, the first number 4864 is

• not divisible by 3, because 4 + 8 + 6 + 4 ==> 22
• divisible by 4, because the last two digits 64 is divisible by 4.

To be 4864 x 9P2 divisible by 12, 9P2 must be divisible by 3.

9 + P + 2 ==> 11 + P

If p = 1, then we will get 12. It is divisible by 3.So, the required number is 1.

Problem 3 :

Consider the numbers of the form 3__8. Which digits could be put in place of ___.So that the number 3___8 is :

a) even  b) divisible by 3  c) divisible by 4

Solution :

a) even

The given number 3__8 is already a even number, because it ends with 8.

So, any number between 0, 1, 2, ...........9 can be filled in the place of ___.

b) divisible by 3

In a number, if the sum of all the digits is divisible by 3 or a multiple of 3, then the number is divisible by 3.

Let x be the unknown.

Add all the digits in the number 3x8.

3 + x + 8   = 11

x = 1

3 + 1 + 8 = 12

So, the number to be filled in the place of ___ is 1.

c) divisible by 4

In a number, if the last two digits are zeroes or the number formed by the last 2 digits is divisible by 4, then the number is divisible by 4.

Let x be the unknown.

3x8

Put x = 2

328

Considering the last two digits, 28 is divisible by 4.

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