Exceptional Solution: Finding the Largest 5-Digit Number Exactly Divisible by 93

Understanding divisibility rules and how to find the largest 5-digit number exactly divisible by a given number can enhance your mathematical skills and problem-solving abilities. In this article, we will explore this concept in detail, specifically focusing on finding the largest 5-digit number exactly divisible by 93, along with clear examples and step-by-step explanations.

Introduction to Divisibility

Divisibility is a fundamental concept in mathematics that deals with the ability of a number to be divided evenly by another number. When a number is exactly divisible by another, it leaves no remainder. The problem at hand is to identify the largest 5-digit number that perfectly divides by 93 without leaving any remainder.

Identifying the Largest 5-Digit Number

The largest 5-digit number is 99999.

When 99999 is divided by 93, the remainder is 24. This information is crucial because it helps us find the largest 5-digit number that is exactly divisible by 93. To find this, we subtract the remainder from the largest 5-digit number:

Step-by-Step Calculation

Step 1: Identify the largest 5-digit number.

Step 2: Determine the remainder when the largest 5-digit number is divided by 93.

Step 3: Subtract the remainder from the largest 5-digit number.

Let's break this down using the given example:

Example 1

99999 ÷ 93  1075 with a remainder of 2499999 - 24  99975

Example 2

Another way to approach this problem is by using division:

100000 ÷ 93  1075.261075 × 93  99975

Thus, we get 99975, which is the largest 5-digit number exactly divisible by 93.

General Approach to Finding the Largest 5-Digit Number Divisible by Any Divisor

The steps to find the largest 5-digit number exactly divisible by any given divisor (such as 93) are:

Find the largest 5-digit number (99999).

Divide the largest 5-digit number by the divisor and note the quotient and the remainder.

Subtract the remainder from the largest 5-digit number to get the answer.

Meta Title: The Largest 5-Digit Number Exactly Divisible by 93

Meta Description: Learn how to find the largest 5-digit number exactly divisible by 93. Understand the process step-by-step with detailed examples and explanations.

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Conclusion

By understanding the process of finding the largest 5-digit number exactly divisible by 93, you can apply this to similar problems involving other divisors. This knowledge is not only beneficial for academic purposes but also for enhancing your problem-solving skills in practical applications.