Question

N is a 1001 digit number consisting of 1001 sevens. What is the remainder when n is divided by 1001?

Answer 1

The remainder after dividing 77777...   by 1001 = 700

Step-by-step explanation:

N is a 1001 digit number (given)

It consists of 1001 times 7.

So N = 7777777.......... (1001 times)

If we start dividing 77777... by 1001 once by simple school level division method.

    1001   (Divisor)    )   7777..........(1001 times) (dividend)    (  777 (quotient)

Dividing first 4 digits   -7007                                

                               =    07707

( again dividing)           - 7007

                                      07007                    

 ( again dividing)           00000

So, This is the cyclic rotation of getting 0 reminder for every 6th digit.

Like this way in total of 1001 digits,

$\frac{\textbf{\large 1001}}{\textbf{\large 6}} =\textbf{\large 166} + \frac{\textbf{\large 5}}{\textbf{\large 6}}$      

5 digits will remain out of cycle.

SO, dividing 77777 (5 digits) by 1001 we get,

$\frac{\textbf{\large 77777}}{\textbf{\large 1001}} =\textbf{\large 77} + \frac{\textbf{\large 700}}{\textbf{\large 1001}}$

here remainder is 700.

$\textbf{\Large So, the remainder after dividing 77777...by 1001 = 700}$

Answer 2

Answer:

N is a 1001 digit number (given)

It consists of 1001 times 7.

So N = 7777777.......... (1001 times)

If we start dividing 77777... by 1001 once by simple school level division method.

1001 (Divisor) ) 7777..........(1001 times) (dividend) ( 777 (quotient)

Dividing first 4 digits -7007

= 07707

( again dividing) - 7007

07007

( again dividing) 00000

So, This is the cyclic rotation of getting 0 reminder for every 6th digit.

Like this way in total of 1001 digits,

\frac{\textbf{\large 1001}}{\textbf{\large 6}} =\textbf{\large 166} + \frac{\textbf{\large 5}}{\textbf{\large 6}}

6

1001

=166+

6

5

5 digits will remain out of cycle.

SO, dividing 77777 (5 digits) by 1001 we get,

\frac{\textbf{\large 77777}}{\textbf{\large 1001}} =\textbf{\large 77} + \frac{\textbf{\large 700}}{\textbf{\large 1001}}

1001

77777

=77+

1001

700

here remainder is 700.