+0

# Can you predict the remainder when 111…1 (100 ones) is divided by 1111111

0
129
1

We have 111...11 a hundred times.

We begin with 1 in our quotient. We have 93 ones remaining. We add six zeros according to the division algorithm to get 1000000 in our quotient. We add another one to get 10000001 in our quotient and we have 86 ones remaining. We see that we get the following answer by the same logic : 1000000100000010000001...1000001 (14 ones because 7*14 = 98 ones taken out so we have 11 left as a remainder)

My question is not on the remainder but on the way the quotient is presented : Why do we say : 1000000100000010000001...100000100 is the quotient and not 1000000100000010000001...10000010 with only one zero at the end ? According to the division algorithm shouldn't I need only one zero to make "11" go down before hitting the decimals ?

Thanks

Guest Jul 5, 2017
Sort:

#1
0

100 "1s" mod 1,111,111 = 11. And it stands to reason since 98 "1s" will divide 1,111,111 evenly with no remainder. So adding two more "1s" will leave you with a remainder of 11.

The quotient of your division will be the bold number, and the fraction after the decimal point, the remainder of 11.

1 000 000 100 000 010 000 001 000 000 100 000 010 000 001 000 000 100 000 010 000 001 000 000 100 000 010 000 001 000 000 100.0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 0990000099 0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 0990000099 0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 0990000099 0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 0990000099 0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 0990000099 0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 0990000099 0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 0990000099 0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 0990000099 0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 0990000099 0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 0990000099 0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 0990000099 0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 0990000099 0000099000 0099000009 9000009900 0009900000 9900000990 0000990000 099......etc.

Guest Jul 5, 2017

### 8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details