Question

Which number is divisible by 8?
A) 1638
B) 2648
C) 2564
D) 3126

Answer 1

Hint:
Here, we are asked to find which number from the given options is divisible by 8.
Thus, divide each number in the options by 8.
If the remainder of any number when divided by any other number is 0, then that number is divisible by the other number.
Hence choose the correct option.

Complete step by step solution:
Here, we are asked to find which number from the given options is divisible by 8.
So, we will divide each number in the options by 8 and check whether we get the remainder as 0.
If the remainder of any number when divided by any other number is 0, then that number is divisible by the other number.
Firstly, in option (A) the number given is 1638.
So, dividing 1638 by 8 gives

Here, when dividing 1638 by 8, we get 6 as a remainder.
So, 1638 is not divisible by 8.
In option (B) the number given is 2648.
So, dividing 2648 by 8 gives

Here, when dividing 1638 by 8, we get 0 as a remainder.
So, 2648 is divisible by 8.
Thus, option (B) is correct.
For further confirmation, we will also divide remaining two numbers by 8 and observe whether they give out remainder as 0 or not.
So, dividing 2564 by 8 gives

Here, when dividing 2564 by 8, we get 4 as a remainder.
So, 2564 is not divisible by 8.
Also, dividing 3126 by 8 gives

Here, when dividing 3126 by 8, we get 6 as a remainder.
So, 3126 is not divisible by 8.

Thus, only option (B) is the correct answer.

Note:
Short-cut method:
If the number formed by the last three digits of a number, which is formed by 4 or more digits, is divisible by 8, then the number is always divisible by 8 no matter what digits are at the remaining places other than the last three places.
For example, here the option (B) 2648 is divisible by 8.
Now, to find out whether 2648 is divisible by 8, take the last three digits of it i.e. 6, 4 and 8 and thus form a number by these digits i.e. 648.
If 648 is divisible by 8, then no matter what number is in the place of 2 in the number 2648, it would be divisible by 8.
So,

Thus, 648 is divisible by 8.
So, 2648 must be divisible by 8. Also, 1648, 3648, 134648 and other similar numbers which have 648 at their last three places are also divisible by 8.