777 divided by a number

[yogami]

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+)

[tohellandback]

IMO 4) 5
numbers are 100,140,175,350.700
level650-700,I guess

[tohellandback]

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.

[anayak]

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.

[tohellandback]

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

[ssmiles08]

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