Allied & ICAR Exam Bank • ALLIED_2167 NAT • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

The remainder when $3^{100}$ is divided by 7 is:

Answer Key:

4

Step-by-Step Solution & Explanation

By Fermat's Little Theorem, $3^6 \equiv 1 \pmod 7$. $100 = 6 \times 16 + 4$. $3^{100} \equiv 3^4 = 81 \pmod 7$. $81 = 7 \times 11 + 4$. Remainder is 4.
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