Find the greatest 4 digit number which is exactly divisible by 13?

Appeared in: RRB Staff Nurse Kolkata-2015

Explanation

The largest 4-digit number is 9999.
To find the largest number divisible by 13, we divide 9999 by 13 and find the remainder.
Dividing 9999 by 13 gives a quotient of 769 and a remainder of 2.
Subtracting the remainder from 9999 gives the required number: 9999 - 2 = 9997.
Therefore, 9997 is the largest 4-digit number that is perfectly divisible by 13.

Option A: When 9991 is divided by 13, it leaves a remainder of 7. A number that is exactly divisible must have a remainder of 0.
Option C: When 9996 is divided by 13, it leaves a remainder of 12. For a number to be exactly divisible, the remainder must be 0.
Option D: When 9993 is divided by 13, it leaves a remainder of 9. A number that is exactly divisible must have a remainder of 0.

Visual 1: Flowchart - A flowchart illustrating the step-by-step process: Start with the largest 4-digit number (9999) → Divide by 13 → Find the remainder (2) → Subtract the remainder from 9999 → Arrive at the final answer (9997).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Finding the largest n-digit number divisible by a given number as background academic context rather than a clinical decision trigger.
This question tests basic mathematical aptitude, a foundational skill for various calculations in nursing, such as determining correct drug dosages and setting IV drip rates.
Developing strong logical reasoning and problem-solving skills through such questions is essential for making quick, accurate decisions in clinical settings.
What if the question asked for the smallest 4-digit number divisible by 13? The approach would change. You would find the remainder when the smallest 4-digit number (1000) is divided by 13 (which is 12). Then, you would add (13 - 12) = 1 to 1000, making the answer 1001.

How to Approach the Question

First, identify the core task from the question: Find the 'greatest 4-digit number' that is 'exactly divisible by 13'.
Recall or determine the largest 4-digit number, which is 9999.
Understand the principle: For a number to be 'exactly divisible' by another, the remainder after division must be zero.
Execute the main calculation: Divide 9999 by 13.
Focus on the remainder of this division. The remainder is the amount by which 9999 exceeds a multiple of 13.
Subtract this remainder from 9999. The result will be the largest possible 4-digit number that is a perfect multiple of 13.

Concept Tested & Keywords

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Practise the full RRB Staff Nurse Kolkata-2015

Attempt every question from this paper in a timed mock, then review the full solution for each one.