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When 777 is divided by a positive integer n, the remainder

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When 777 is divided by a positive integer n, the remainder [#permalink] New post 07 Jul 2008, 09:42
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When 777 is divided by a positive integer n, the remainder is 77. How many possibilites are there for n?

A. 2
B. 3
C. 4
D. 5
E. 6
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Re: When 777 is divided by a positive integer n... [#permalink] New post 07 Jul 2008, 09:55
Hi think that the ans is 5
n can be 100, 140,175, 350,700,
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Re: When 777 is divided by a positive integer n... [#permalink] New post 07 Jul 2008, 09:56
BG wrote:
Hi think that the ans is 5
n can be 100, 140,175, 350,700,


Could you explain the way you did it? :?:
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Re: When 777 is divided by a positive integer n... [#permalink] New post 07 Jul 2008, 10:02
Any factor of 700 greater than 100. If you do the prime factorization of 700, you'll get: 2, 2, 5, 5, 7. With those primes, you can only build the numbers BG said.
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Re: When 777 is divided by a positive integer n... [#permalink] New post 07 Jul 2008, 10:21
Start from the largest divisor.
Then check all the multiple of biggest divisor (700 in this case), which are greater than 77 but less than biggest divisors)

100,140,175,350,700

IMO D.

Last edited by abhijit_sen on 07 Jul 2008, 10:39, edited 1 time in total.
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Re: When 777 is divided by a positive integer n... [#permalink] New post 07 Jul 2008, 10:29
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I wrote out all of the factors of 700 like 1..700, 2...350, 4...175, 5...140, 7...100, 10...70, STOP

I did this down to 10...70, because I realized at the point where you get blow the remainder in quesiton, you don't have a remainder of 77 anymore...so it's 100, 140, 175, 350, and 700...total of 5 in all.
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Re: When 777 is divided by a positive integer n... [#permalink] New post 07 Jul 2008, 10:40
nirimblf wrote:
When 777 is divided by a positive integer n, the remainder is 77. How many possibilites are there for n?

A. 2
B. 3
C. 4
D. 5
E. 6


777 = k*n + 77 -> n > 77, k*n = 700 = 7*(2^2)*(5^2)

1) without 7 -> only (2^2)*(5^2) = 100 because otherwise below 77
2) with 7 -> 7*(2^x1)*(5^x2) > 77 -> 7*(2^2)*(5^2), 7^(2^2)*5 //with 2^2// 7^2*(5^2) //with 2^1 and 7^5^2 //with 2^0
1+4 = 5 -> D
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Re: When 777 is divided by a positive integer n... [#permalink] New post 07 Jul 2008, 10:44
jallenmorris wrote:
I wrote out all of the factors of 700 like 1..700, 2...350, 4...175, 5...140, 7...100, 10...70, STOP

I did this down to 10...70, because I realized at the point where you get blow the remainder in quesiton, you don't have a remainder of 77 anymore...so it's 100, 140, 175, 350, and 700...total of 5 in all.


Thanks, that's an explanation I can easily understand. +1.
Re: When 777 is divided by a positive integer n...   [#permalink] 07 Jul 2008, 10:44
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