GRE Quant: Units Digit in Large Multiplication

Units digit questions in large multiplication focus on tracking only the units digit of each term and carrying forward just that digit through the multiplication. You isolate the last digit at every step, multiply only those units digits, and ignore the remaining value since it does not affect the final outcome. This method brings clarity and efficiency to this specific GRE Quant question type. The following video, part of the GRE prep course by Experts’ Global, explains this idea in a clear, structured, and practical manner and shows how to apply the method across GRE-style problems involving large products.

 

Underlying Concept in Finding Units Digit in Large Multiplication

To find the last digit of a product, you do not need to multiply the entire numbers. Instead, you only need to multiply the digits located in the units places.

This concept can be simplified across different levels of the calculation:

• For the multiplication 112 x 113, the result’s last digit is determined by the last digits of the factors.
• This is equivalent to looking at 12 x 13.
• Ultimately, you only need to calculate 2 x 3.

Because 2 x 3 = 6, the last digit of 112 x 113 is 6.

---

Application of the Concept…

To find the last digit of a large product, you only need to focus on the last digits of each individual number.

Core Method

For the expression: 343 x 536 x 6742 x 753 x 879 x 545 x 787

You can determine the final digit by multiplying the units digits of each number in sequence: 3 x 6 x 2 x 3 x 9 x 5 x 7

Step-by-Step Calculation

• 3 x 6 = 18 (last digit is 8)
• 8 x 2 = 16 (last digit is 6)
• 6 x 3 = 18 (last digit is 8)
• 8 x 9 = 72 (last digit is 2)
• 2 x 5 = 10 (last digit is 0)
• 0 x 7 = 0 (last digit is 0)

The final answer for the last digit is 0.

Efficiency Shortcut

A faster way to solve this is to look for specific pairs. If the set of numbers contains both a ‘2’ and a ‘5’ as last digits, their product will result in a ‘0’.

Once a 0 appears as a last digit in a multiplication chain, the final digit for the entire product will inevitably be 0.

---

Conceptual Practice Set…

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

 

To find the last digit of a multiplication product, you only need to multiply the last digits of each number in the sequence. If a product results in a two-digit number, you only carry forward its last digit to the next multiplication.

 

Question 1

324 x 537 x 4356 x 563 x 642 x 798

Explanation

• Multiply 4 x 7 = 28 (Use 8)
• Multiply 8 x 6 = 48 (Use 8)
• Multiply 8 x 3 = 24 (Use 4)
• Multiply 4 x 2 = 8
• Multiply 8 x 8 = 64 (Use 4)

Correct Answer: 4

 

Question 2

528 x 797 x 534 x 989 x 757 x 643

Explanation

• Multiply 8 x 7 = 56 (Use 6)
• Multiply 6 x 4 = 24 (Use 4)
• Multiply 4 x 9 = 36 (Use 6)
• Multiply 6 x 7 = 42 (Use 2)
• Multiply 2 x 3 = 6

Correct Answer: 6

 

Question 3

393 x 435 x 367 x 899 x 6357 x 844

Explanation

• Notice that there is a number ending in 5 (435) and a number ending in an even digit (844).
• Any number ending in 5 multiplied by any even number results in a product ending in 0.
• Once a 0 is at the end, the final result will always end in 0.

Correct Answer: 0

 

Question 4

893 x 437 x 5671 x 899 x 6353

Explanation

• Multiply 3 x 7 = 21 (Use 1)
• Multiply 1 x 1 = 1
• Multiply 1 x 9 = 9
• Multiply 9 x 3 = 27 (Use 7)

Correct Answer: 7

 

Question 5

797 x 434 x 567 x 897 x 6352

Explanation

• Multiply 7 x 4 = 28 (Use 8)
• Multiply 8 x 7 = 56 (Use 6)
• Multiply 6 x 7 = 42 (Use 2)
• Multiply 2 x 2 = 4

Correct Answer: 4

---

For Further GRE Prep and Practice…

Free full length GRE diagnostic mock

15 full length GRE practice tests

60 sectional GRE practice tests

All-inclusive GRE prep course online

GRE prep bundled with admission consulting