GRE Quant: Last Two Digits in Large Multiplication

Last two digits questions in large multiplication focus on tracking only the final two digits of each term and carrying forward just those digits through the multiplication process. You isolate the last two digits at every step, multiply only those parts, and discard the remaining value since it does not influence the final result. This approach keeps the work precise and efficient for this specific GRE Quant question type. The following video, part of our end-to-end GRE prep course, explains this method in a clear, structured, and practical way and demonstrates how to apply it smoothly to GRE-style problems involving large products.

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Underlying Concept: Last 2 Digits

Last two digits

To find the last two digits of a product of several large numbers, you can focus specifically on the last two digits of each individual term.

The Problem

Calculate the last 2 digits of: 787 x 625 x 579 x 347 x 520 x 777.

The Strategy

While you could multiply the last two digits of every number in the sequence, this is often time-consuming. Instead, look for “friendly numbers” or a “catch” that simplifies the calculation.

The Shortcut

In this specific sequence, two numbers provide a significant shortcut:

The last two digits of 625 are 25.
The last two digits of 520 are 20.

When you multiply these two components: 25 x 20 = 500

The last two digits of this intermediate product are 00.

The Final Result

Because any number multiplied by a value ending in 00 will also end in 00, the calculation for the entire expression becomes: 00 x 87 x 79 x 47 x 77 = 00

Therefore, the last two digits of the entire product are 00.

A Conceptual Example: Last 2 Digits

A conceptual example of Last two digits

To find the last two digits of the product of a series of numbers, you can isolate the relevant trailing digits from each term to simplify the calculation.

Problem

Find the last two digits of: 989 * 627 * 571 * 342 * 759 * 715

Step 1: Determine the Last Digit

Focus on the last two digits of the final two numbers: 42 and 15. Multiplying these gives: 42 * 15 = 630. Because this product ends in 0, the last digit of the entire sequence is 0.

Step 2: Determine the Second to Last Digit

The remaining tens and units digits from the product are used to find the next position. Based on the method shown, the calculation focuses on the product of the units digits of the preceding numbers and the remaining value from the previous step: 3 * 9 * 7 * 1 * 9 This simplifies to: 27 * 63

Conclusion

The resulting last two digits of the original product are 10.

A Conceptual Practice Set

A conceptual practice set

For a detailed explanation, please refer the video presented earlier on this page.

Question 1

2987 * 3073 * 5075 * 389 * 508 Answer options: 00

Explanation

To find the last two digits, look for factors of 100 (which is 4 * 25) within the numbers.

5075 is a multiple of 25 (since 75 is divisible by 25).
508 is a multiple of 4 (since 08 is divisible by 4). Because the expression contains both a multiple of 25 and a multiple of 4, the product must be a multiple of 100. Any multiple of 100 ends in 00.

Correct Answer: 00

Question 2

5783 * 6739 * 8753 * 2025 * 8769 * 206 Answer options: 50

Explanation

Identify factors of 50 (which is 2 * 25) or 100.

2025 is a multiple of 25.
206 is a multiple of 2. Multiplying a multiple of 25 by an even number (2) results in a multiple of 50. This means the product must end in either 00 or 50. The other numbers in the set (5783, 6739, 8753, 8769) are all odd. Since there is only one even number (206) and it is not a multiple of 4, the product is a multiple of 50 but not 100.

Correct Answer: 50

Question 3

267 * 873 * 670 * 653 * 594 Answer options: 40

Explanation

Focus on the last digits and the tens place.

670 provides a 0 at the end.
To find the second to last digit, multiply the remaining last digits: 7 * 3 * 7 * 3 * 4.
7 * 3 = 21 (ends in 1).
7 * 3 = 21 (ends in 1).
1 * 1 * 4 = 4. The product of the units digits of the other numbers and the tens digit of 670 results in 4. Combined with the 0 from 670, the last two digits are 40.

Correct Answer: 40