How to Find the Remainder of a Large Multiplication on the GMAT?

Short Answer

To find the remainder of a large product, replace each number with its remainder when divided by the divisor, then multiply those remainders. For example, (23 × 41 × 67) ÷ 5: 23 leaves 3, 41 leaves 1, 67 leaves 2. Multiply 3 × 1 × 2 = 6. Dividing 6 by 5 leaves remainder 1. Thus, the overall remainder is 1.

 

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In your GMAT preparation, remainder questions open a fascinating window into how simple rules can simplify large expressions. Instead of multiplying huge numbers, you only need to track remainders and combine them smartly. This approach saves time, ensures accuracy, and builds logical clarity. Practicing with GMAT practice tests helps you apply these rules under exam-like conditions until they feel natural. What once seemed like a long calculation turns into a quick, structured process, showing how the GMAT rewards clarity of thought and pattern recognition.

 

Understanding How to Find the Remainder of a Large Product

When faced with remainder problems, you do not need to multiply large numbers fully. The key is to simplify step by step. Divide each term by the divisor, note the remainder, and multiply these smaller values together. Finally, divide the result by the same divisor to get the overall remainder.

For example, (14 × 17) ÷ 5: 14 leaves remainder 4, 17 leaves remainder 2. Multiply 4 × 2 = 8, and dividing 8 by 5 leaves remainder 3. This simple process avoids large multiplication and shows the efficiency of the method.

Remainders When Dividing by 2, 5, or 10

For 2, 5, and 10, only the last digit matters.

• If the last digit is even, remainder with 2 is 0. If odd, remainder is 1.
• If the last digit is 0 or 5, remainder with 5 is 0. Otherwise, remainder is that digit itself.
• If the last digit is 0, remainder with 10 is 0. Otherwise, remainder is simply that digit.

Example: 437 → last digit 7 → remainder 1 with 2, remainder 2 with 5, remainder 7 with 10.

Remainders When Dividing by 4, 25, or 50

For these divisors, look at the last two digits of the number.

• 327 → last two digits 27 → remainder with 4 is 3.
• 845 → last two digits 45 → remainder with 25 is 20.
• 152 → last two digits 52 → remainder with 50 is 2.

In products, reduce each number first, then multiply the remainders.
Example: Remainders 1, 2, 2, 3, and 4 → product = 48. Dividing 48 by 25 leaves remainder 23.

Remainders When Dividing by 3 or 9

For 3 and 9, use the digit-sum rule.

• Add the digits of the number.
• Divide the sum by 3 or 9.
• Example: 457 → digit sum = 16.
• 16 ÷ 3 → remainder 1.
• 16 ÷ 9 → remainder 7.

This method avoids long division and works quickly for very large numbers.

Remainders When Dividing by 7

There is no fixed shortcut for 7. Here, divide directly and reduce to smaller cases.

• 420 is divisible by 7.
• 427 leaves remainder 1.
• 428 leaves remainder 2.

On the GMAT, numbers given are usually “friendly,” so simple checking is enough.

The Bigger Lesson in GMAT Thinking

These remainder problems are not just about numbers. They teach you to look for patterns, avoid brute force, and trust the structure hidden in questions. By breaking down large expressions into small remainders, you practice the kind of analytical thinking that the GMAT values deeply. And these insights extend far beyond the test, training you to see clarity where others see confusion. Such habits not only build your confidence in math but also strengthen the analytical presence you carry into MBA admissions journey and, eventually, into leadership roles.

Parting Thought

Remainder problems remind us that even the largest challenges can be broken into smaller, manageable parts. The GMAT prep is never about brute calculation; it is about clarity, patience, and seeing structure in the midst of complexity. When you learn to simplify, every problem becomes approachable. This habit extends far beyond mathematics. In life and in the MBA journey, success often lies in breaking overwhelming goals into smaller, clear steps. Just as remainders guide you through huge numbers, disciplined reasoning guides you through uncertainty, giving you the confidence to face both exams and real challenges with calm precision.