Question

What least number should be replaced for * so that the number 76102*3 is exactly divisible by 9 ?
5
6
7
8​

Answer 1

Step-by-step explanation:

Complete step-by-step solution:

Given the number 67301∗2 .

We have to find the number ∗ so that 67301∗2 is exactly divisible by nine.

If a number is divisible by nine, then the sum of its digits must also be divisible by nine.

So we have to find ∗ such that, 6+7+3+0+1+∗+2 is a multiple of nine.

That is, 19+∗ is a multiple of nine.

We know the least multiple of nine greater than or equal to 19 is 27.

So we can write, 19+∗=27

This gives, ∗=27−19=8

So the least number that can be replaced by ∗ so that 67301∗2 is exactly divisible by nine is 8.

∴ The answer is 8.

Answer 2

Answer:

A number is divisible by 9 if the sum of its digits is divisible by 9.

Now, Sum of the digits in given number = 7+6+1+0+2+3 = 19, which is not divisible by 9.

But, if we add 8 to this sum, it becomes 19+8=27, which is divisible by 9

So, 7610283 is divisible by 9

So, the least number is 8 which should replace for ∗ in the given number.