Find the unit digit in the product (365 × 659 × 771)

Question: Find the Unit Digit of (3^65 * 6^59 * 7^71)

To find the unit digit of a product, we find the unit digit of each power individually and multiply them.

Step-by-Step Analysis:

1. 3^65: The powers of 3 follow a cycle of four: 3, 9, 7, 1.

   • 65 / 4 = 16 remainder 1.

   • The unit digit is the 1st in the cycle: 3.

2. 6^59: The powers of 6 always end in 6 (6^1=6, 6^2=36, etc.).

3. 7^71: The powers of 7 follow a cycle of four: 7, 9, 3, 1.

   • 71 / 4 = 17 remainder 3.

   • The unit digit is the 3rd in the cycle: 3.

Final Calculation:

• Multiply the unit digits: 3 * 6 * 3 = 54.

• The unit digit of the final product is 4.

Conclusion: Option B (4) is correct.