Question

18. What is the greatest number of 4-
digits which is exactly divisible by
97 ?
(Sainik School, 2006-07]​

Answer 1

Step-by-step explanation:

We know that largest four digit number is 9999.

⇒ So, when we divide 9999 by 97, we get 103.08 as a remainder.

∴ The largest 4 digit number exactly divisible by 97 = 9999−103.08 = 9895.92

Answer 2

The number is 9991

Given :

• The number has 4 digits
• The number is exactly divisible by 97

To find : The maximum possible number which matches the given criteria.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the required number)

In general, the largest number which has four digits is 9999

Now,

If we take 9999 as the dividend and 97 as divisor then

• Quotient = 103
• Remainder = 8

So, if we subtract the remainder from the dividend, the newly formed number (obtained from subtraction) will become divisible by the previous divisor.

The required number = Dividend - Remainder = 9999-8 = 9991

Now,

If we take 9991 as the dividend and 97 as divisor then,

• Quotient = 9991
• Remainder = 0

Which implies 9991 is the required number.

(It is also the maximum number which matches all the requirements, because the next number which is divisible by 97 has five digits. i.e. next divisible number, 9991+97 = 10088 has five digits)

Hence, the number is 9991