Question

The remainder when $26^{60}$ is divided by 5 equals:

• A. 0
• B. 1
• C. 2
• D. None of these

Hint:

Always reduce the base modulo the divisor first; it can instantly simplify huge exponent problems.

Answer 1

The Correct Option is B

We solve using modular arithmetic. First, reduce the base: $26 \div 5$ leaves remainder 1, so $26 \equiv 1 \ (\text{mod } 5)$.
Thus, $26^{60} \equiv 1^{60} \ (\text{mod } 5)$. Since $1^{60} = 1$, the remainder when $26^{60}$ is divided by 5 is 1.
No matter how large the exponent, once the base is congruent to 1 modulo 5, all powers will leave remainder 1.
Therefore, answer is (B) 1.