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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Find the remainder when
$X = 1! + 2! + 3! + \cdots + 100!$
is divided by $240$.
Solution
For $n \ge 6$,$n!$ is divisible by $240 = 2^4 \cdot 3 \cdot 5$.
Thus only first 5 factorials matter:
$1! + 2! + 3! + 4! + 5!$
$= 1 + 2 + 6 + 24 + 120 = 153$
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