Write the remainder obtained when 1! + 2! + 3! + ... + 200! is di… - Vidyadip

Question

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

✓

Answer

First we will find the least factorial term divisible by 14. As 7!=7 × 6 × 5! is divisible by 14 leaving remainder zero. Hence terms 7! onwards can be written as multiple of 7!. 8!=8 × 7!, 9! = 9 × 8 × 7!... like ways 200! can also be written as multiple of 7!. So all the terms 7! onwards are divisible by 14 leaving remainder zero. = 1! + 2! + 3! + 4! + 5! + 6! = 1 + 2 + 6 + 24 + 120 + 720 = 873 Hence remainder obtained when 1! + 2! + 3! + ….+ 200! is divided by 14 is 5.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 1 marks)" from Permutations→Permutations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\sin\theta_1+\sin\theta_2+\sin\theta_3=3,$ then write the valuue of $\cos\theta_1+\cos\theta_2+\cos\theta_3.$

Write $\sum\limits_\text{r=0}^\text{m}\ {^\text{n+r}}\text{C}_{\text{r}}$ in the simplified form.

If A is any set, prove that: $\text{A}\subseteq\phi\Leftrightarrow\text{A}=\phi.$

If P = {a, b, c} and Q = {r}, form the sets P $\times$ Q and Q $\times$ P. Are these two products equal?

If second, third and sixth term of an A.P. are consecutive terms of a G.P., write the common ratio of G.P.

Three coins are tossed Describe. Two events A and B which are mutually exclusive.

If $A=\left\{(x, y): y=e^x, x \in R\right\}$ and $B=\left\{(x, y): e^{-x}, x \in R\right\}$, then write $A \cap B$.

Find the derivative of the function $f(x) = 2x^2 + 3x - 5 at x = - 1$. Also, prove that f'(0) + 3f'(-1) = 0.

Is the collection of ten most talented writers of Indiaset? Justify your answer

If A = {1, 2, 3}, B = {4, 5, 6}, the given following are relations from A to B? Give reason in support of your answer.{(4, 2), (4, 3), (5, 1)}