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

Question

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

BG · Answer

Hi think that the ans is 5
n can be 100, 140,175, 350,700,

nirimblf · Answer

Could you explain the way you did it? :?:

asdert · Answer

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.

abhijit_sen · Answer

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.

jallenmorris · Answer

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.

maratikus · Answer

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

nirimblf · Answer

Thanks, that's an explanation I can easily understand. +1.

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

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