43^256*57^343 what is unit digit of product?
2025
43^256*57^343 what is unit digit of product?
- A.
3
- B.
1
- C.
2
- D.
4
Attempted by 77 students.
Show answer & explanation
Correct answer: A
Key idea: use the units digits and their repeating cycles.
Find the units digit of 43^256. The units digit of the base 43 is 3. Powers of 3 repeat every 4: 3, 9, 7, 1. Compute 256 mod 4 = 0, which corresponds to the 4th value in the cycle, 1. So units digit of 43^256 is 1.
Find the units digit of 57^343. The units digit of the base 57 is 7. Powers of 7 repeat every 4: 7, 9, 3, 1. Compute 343 mod 4 = 3, so take the 3rd value in the cycle, 3. Thus units digit of 57^343 is 3.
Multiply the units digits: 1 × 3 = 3. Therefore the units digit of the product 43^256 × 57^343 is 3.
Answer: 3