What is the units digit of 7^105?

Concept / Approach

• Units digits of powers of 7 cycle every 4: 7, 9, 3, 1, then repeat.

Step-by-step calculationCompute exponent modulo 4: 105 mod 4 = 1Position 1 in the cycle corresponds to units digit 7.

Common pitfallUsing 105 ÷ 4 = 26.25 and rounding incorrectly. Only the remainder matters.

Final Answer7