43^256 * 57^343 what is the unit digit of product?
2025
43^256 * 57^343 what is the unit digit of product?
- A.
3
- B.
1
- C.
2
- D.
4
Attempted by 11 students.
Show answer & explanation
Correct answer: A
Key idea: only the units digits of the factors determine the units digit of the product.
Step 1: Reduce each base to its units digit: 43 → 3, 57 → 7.
Step 2: Find the units-digit cycle for powers of 3: 3, 9, 7, 1 (cycle length 4). Since 256 ≡ 0 (mod 4), 3^256 has units digit 1.
Step 3: Find the units-digit cycle for powers of 7: 7, 9, 3, 1 (cycle length 4). Since 343 ≡ 3 (mod 4), 7^343 has units digit 3.
Step 4: Multiply the resulting units digits: 1 × 3 = 3. Therefore the units digit of 43^256 × 57^343 is 3.
Answer: 3