The question asks for the least number consisting of five digits that is divisible by 97 and the sum of its digits. Let's break down the steps to find this number and its sum of digits.

Finding the Least Five-Digit Number

First, we need to identify the smallest possible number that has five digits. This number is 10000.

Checking Divisibility by 97

Next, we need to determine if 10000 is divisible by 97. To do this, we perform division with remainder.

We divide 10000 by 97:

\(10000 \div 97\)

Using long division or a calculator, we find:

\(10000 = 97 \times 103 + 9\)

This means that when 10000 is divided by 97, the quotient is 103, and the remainder is 9. Since the remainder is not 0, 10000 is not divisible by 97.

Finding the Next Multiple of 97

To find the least five-digit number that IS divisible by 97, we need to find the smallest multiple of 97 that is greater than or equal to 10000.

Since \(10000 = 97 \times 103 + 9\), 10000 is 9 more than a multiple of 97 (which is \(97 \times 103 = 9991\)).

To get to the next multiple of 97, we need to add the difference between the divisor (97) and the remainder (9) to 10000.

Amount to add = Divisor - Remainder

Amount to add = \(97 - 9 = 88\)

So, the least number consisting of five digits that is divisible by 97 is:

Least five-digit number divisible by 97 = \(10000 + 88 = 10088\)

Verifying the Number

Let's verify if 10088 is divisible by 97:

\(10088 \div 97\)

\(10088 = 97 \times 104\)

The division results in an integer quotient (104) with no remainder, confirming that 10088 is divisible by 97. It is also the smallest such five-digit number because 9991 is a four-digit number.

Therefore, the number x is 10088.

Calculating the Sum of Digits of x

Now, we need to find the sum of the digits of x, which is 10088.

Sum of digits = \(1 + 0 + 0 + 8 + 8\)

Sum of digits = \(17\)

Summary of Steps

The sum of digits of the least five-digit number divisible by 97 is 17.

Revision Table - Number Divisibility Concepts

Additional Information - Properties of Numbers

Understanding properties of numbers and divisibility rules is key to solving problems like this. While there isn't a simple divisibility rule for 97, the general approach of using division with remainder to find multiples is very useful.

Key points about this problem:

• The smallest five-digit number is 10000.
• To find a multiple of 97 near 10000, we perform division.
• The remainder tells us how far away 10000 is from a multiple of 97.
• Adding (divisor - remainder) to the original number gives the next multiple.
• The sum of digits is a simple arithmetic calculation after finding the number.

This method can be applied to finding the least (or greatest) N-digit number divisible by any given number.