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Seven 7housand

Posted by Atran on July 15, 2010 – 6:06 pm

What is the quotient when  a number made up of one-thousand-and-one sevens  (i.e. 77777777……etc.) is divided by the number 1001?

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This post is under “Mathemagic, MathsChallenge, Tom” and has 14 respond so far.

14 Responds so far- Add one»

1. 1. Jhowmar Said：

hmm well first not that great with taking things down to a mathimatical reasoning also not sure how much to post being the first post don’t want to post the answer if i’m right.

I don’t think you need to use all 100001 7’s to get the answer.

2. 2. Nathan Said：

166 repitions of “777000″ followed by 77700.77777….

3. 3. rick Said：

its 7 you idiots.. i know that and im in 7th grade

4. 4. slavy Said：

Even though this is again arithmetic and so far I have never guessed the correct answer, I will stubbornly try once again and suggest: 166 repetitions of “777000″ followed by 77.(699300) (this is my notation for periodic fraction). If you don’t like the last part – this should be 77.7-(1/1430)…

5. 5. Anonymous Said：

What is the quotient when a number made up of one-thousand-and-one sevens (i.e. 77777777……etc.) is divided by the number 1001?

try long division for an arbitrary long run of 7s /1001

7/1001=0R7
77/1001=0R77
777/1001=0R777
7777/1001=7R770
7707/1001=7R700
7007/1001=7R0

So we can see that the cycle of 000777 repeats every 6 digits. (Leading 0s can be eliminated for the first time)
1001/6=166R5

So for the last 5 7s before the decimal :
7/1001=0R7
77/1001=0R77
777/1001=0R777
7777/1001=7R770
7707/1001=7R700
Decimal Point here
7007/1001=7R0

followed by 000777…

So we could say the number representing the quotient is 777000 repeated 166 times followed by 77.7 followed by 000777 forever

Cam

6. 6. Anoonymous Said：

Goofed on the portion after the decimal. Erred in continuing to carry down 7s as opposed to 0s after the decimal. Now fixed.

What is the quotient when a number made up of one-thousand-and-one sevens (i.e. 77777777……etc.) is divided by the number 1001?

try long division for an arbitrary long run of 7s /1001

7/1001=0R7
77/1001=0R77
777/1001=0R777
7777/1001=7R770
7707/1001=7R700
7007/1001=7R0

So we can see that the cycle of 000777 repeats every 6 digits. (Leading 0s can be eliminated for the first time)
1001/6=166R5

So for the last 5 7s before the decimal :
7/1001=0R7
77/1001=0R77
777/1001=0R777
7777/1001=7R770
7707/1001=7R700
Decimal Point here
7000/1001=6R994
9940/1001=9R931
9310/1001=9R301
3010/1001=3R7
70/1001=0R70
700/1001=0R700

And then it cycles

So we could say the number representing the quotient is 777000 repeated 166 times followed by 77. followed by 699300 forever

Cam

7. 7. Anonymous Said：

My correection post has dissapeared down the black hole….so here’s a repost

Goofed on the portion after the decimal. Erred in continuing to carry down 7s as opposed to 0s after the decimal. Now fixed.

What is the quotient when a number made up of one-thousand-and-one sevens (i.e. 77777777……etc.) is divided by the number 1001?

try long division for an arbitrary long run of 7s /1001

7/1001=0R7
77/1001=0R77
777/1001=0R777
7777/1001=7R770
7707/1001=7R700
7007/1001=7R0

So we can see that the cycle of 000777 repeats every 6 digits. (Leading 0s can be eliminated for the first time)
1001/6=166R5

So for the last 5 7s before the decimal :
7/1001=0R7
77/1001=0R77
777/1001=0R777
7777/1001=7R770
7707/1001=7R700
Decimal Point here
7000/1001=6R994
9940/1001=9R931
9310/1001=9R301
3010/1001=3R7
70/1001=0R70
700/1001=0R700

And then it cycles

So we could say the number representing the quotient is 777000 repeated 166 times followed by 77. followed by 699300 forever

Cam

8. 8. Chris Said：

Hi Cam. You’re missing post is pending approval by Astran. It might have got stuck there as you signed on with Anoonymous (two o’s).

9. 9. Chris Said：

@rick, unless you learn to think, you’ll probably stay in the 7th grade.

10. 10. austyn Said：

its 7 i think

11. 11. Rington Said：

You’re funny, austyn

12. 12. ftawil Said：

1000 od 7 is divisible by 11
1010 is divisible by 11
hence 7777…../1010 = 707070…
& 1001 of 7’s/1010= 707070…….36

13. 13. Spencer Said：

Hi Rick! Im in 7th too.
It is much more complicated than that.
In 1st grade we learned how to add and how to check our work.

1001*7 is not equal to 777777777777777777777777777777777 etc.

Nor is 1001^7