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Evaluate (3459874 * 457832 * 34568) mod 10. Box in your final answer. Remember to show all work.

Evaluate (3459874 * 457832 * 34568) mod 10. Box in your final answer. Remember to show all work.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Evaluate \((3459874 \times 457832 \times 34568) \mod 10\). Box in your final answer. Remember to show all work. **Solution:** To solve the problem, we need to calculate the expression \((3459874 \times 457832 \times 34568)\) and then determine the remainder when this product is divided by 10. **Step-by-step Solution:** 1. **Find the Last Digit of Each Number:** - For 3459874, the last digit is 4. - For 457832, the last digit is 2. - For 34568, the last digit is 8. 2. **Compute the Product of the Last Digits:** - Multiply the last digits: \(4 \times 2 \times 8 = 64\). 3. **Find the Last Digit of the Product:** - The last digit of 64 is 4. 4. **Modulo Operation:** - Since the last digit of the product is 4, \(64 \mod 10 = 4\). 5. **Final Answer:** - The remainder when \(3459874 \times 457832 \times 34568\) is divided by 10 is boxed as follows: \(\boxed{4}\). By following these steps, you can solve similar problems involving large numbers and modulo operations efficiently.
Transcribed Image Text:**Problem Statement:** Evaluate \((3459874 \times 457832 \times 34568) \mod 10\). Box in your final answer. Remember to show all work. **Solution:** To solve the problem, we need to calculate the expression \((3459874 \times 457832 \times 34568)\) and then determine the remainder when this product is divided by 10. **Step-by-step Solution:** 1. **Find the Last Digit of Each Number:** - For 3459874, the last digit is 4. - For 457832, the last digit is 2. - For 34568, the last digit is 8. 2. **Compute the Product of the Last Digits:** - Multiply the last digits: \(4 \times 2 \times 8 = 64\). 3. **Find the Last Digit of the Product:** - The last digit of 64 is 4. 4. **Modulo Operation:** - Since the last digit of the product is 4, \(64 \mod 10 = 4\). 5. **Final Answer:** - The remainder when \(3459874 \times 457832 \times 34568\) is divided by 10 is boxed as follows: \(\boxed{4}\). By following these steps, you can solve similar problems involving large numbers and modulo operations efficiently.
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