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777 divided by a number

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by yogami » Mon Jun 08, 2009 7:21 pm
When 777 is divided by n, a positive integer) the remainder is 77. Howe many possible values are there for n?

1) 2
2) 3
3) 4
4) 5
5) 6

Please post your answer, time taken, and rating (500+/600+/700+/750+)
200 or 800. It don't matter no more.
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by tohellandback » Mon Jun 08, 2009 7:31 pm
IMO 4) 5
numbers are 100,140,175,350.700
level650-700,I guess
The powers of two are bloody impolite!!
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by tohellandback » Mon Jun 08, 2009 7:35 pm
by the way:
the method is:
777=700+77
now we have to find the numbers greater than 77 that evenly divide into 700.
700=7*2^2*5^2
this is how I proceed:
from this you can find the different factors possible which are greater than 77.

Hope it helps.
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by anayak » Mon Jun 08, 2009 7:39 pm
777= an+77
=> an= 777-77= 700

Hence the possible combinations of a and n that can give an=700 are, 10,7,2,35,5,14. Hence I guess the answer is 6.
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by tohellandback » Mon Jun 08, 2009 7:48 pm
Anayak,
I guess you should check your explanation.
There are so many numbers that will NOT give emainder 77.
ex: 70,14,35,50 etc
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by ssmiles08 » Mon Jun 08, 2009 8:04 pm
I got the same as tohellandback (D)

x = QN + R

777 = QN + 77

QN = 700

since n is the divisor, the smallest number n can be is 78, to have a remainder of 77.

so all integer factors of 700 greater than 77 are acceptable:

1 700
2 350
4 175
5 140
7 100
----------
10 70---> doesn't count b/c it is less than 77

So there are 5 factors in total
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