Allied & ICAR Exam Bank • ALLIED_2485 NAT • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

The remainder when $1! + 2! + 3! + 4! + \dots + 100!$ is divided by 12 is:

Answer Key:

9

Step-by-Step Solution & Explanation

For all $n \ge 4$, $n!$ contains factors $3 \times 4 = 12$, so $n! \equiv 0 \pmod{12}$. Sum $\equiv 1! + 2! + 3! = 1 + 2 + 6 = 9 \pmod{12}$. Remainder is 9.
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