Question

Find the smallest number that must be added to 289279 to make it divisible by 8.

Answer 1

Hint: A number is divisible by 8 only if its last three digits are divisible by 8. For the given number, check if its last three digits are divisible by 8 or not. If it is not divisible by 8, find the remainder and adjust it by adding the smallest number to make it divisible by 8.

Complete step-by-step answer:
According to the question, the given number is 289279. We have to check its divisibility by 8.
We know that a number is divisible by 8 only if its last three digits are divisible by 8. For the above number, its last three digits are 279. So we basically have to check the divisibility of 279 by 8.
Off course 279 is not divisible by 8 because it is an add number and any odd number can never be a multiple of 8. So we will find the remainder when 279 is divisible by 8.
$ \Rightarrow 279 = 34 \times 8 + 7$
We can see that when 279 is divided by 8, the quotient is 34 and the remainder is 7.
So to make 279 divisible by 8, we can subtract the remainder 7 from it to get the 34th multiple of 8.
$ \Rightarrow 279 - 7 = 272 = 34 \times 8$
But the question is asking to add the smallest possible number to get the multiple of 8. So instead of subtracting 7, we can also add 1 to 279 to get the 35th multiple of 8.
$ \Rightarrow 279 + 1 = 280 = 35 \times 8$

Thus the smallest number that can be added to 289279 to make it divisible by 8 is 1.

Note: A number is divisible by 2 only if its last digit is divisible by 2. A number is divisible by 4 only if its last two digits are divisible by 4. Similarly, a number is divisible by 8 only if its last three digits are divisible by 8. This can be extended up to any number of digits. In generalization, we can say that a number is divisible by ${2^n}$ only if its last $n$ digits are divisible by ${2^n}$.