# Write the remainder obtained when 1! + 2! + 3! + ...+ 200! is divided by 14.

We can see, from 7! onwards the terms are divisible by 14.

7!=7×6×5×4×3×2×1

=(7×2)×6×5×4×3

=14×360

So, we should consider up to 6! term to obtain the remainder.

Now,

1! + 2! + 3! + 4! + 5! + 6!

= 1 + 2 + 6 + 24 + 120 + 720

= 873

On dividing 873 by 14, we get 5 as remainder.

14×62=868

and 873-868=5

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Circular permutations61 mins
Challenging Quiz on P&C | Test Yourself55 mins
Permutations & Combinations | Analyze your learningFREE Class
Understand Permutations like never before60 mins
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Lecture on Combinations49 mins
Interactive Quiz on Division and distribution of objects17 mins
Interactive Quiz on Combinations-0253 mins
Interactive Quiz on Combinations50 mins
Division and distribution of objects58 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses