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# When the number 777 is divided by the integer N, the remaind

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Re: When the number 777 is divided by the integer N, the remaind  [#permalink]

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02 Oct 2015, 19:50
hatemnag wrote:
please bunuel help me in this. 77/700 = 11/100 is 700 in such case, a possibility for n of the 5 possibility for n ?

Please repost your question. The language is not clear however one thing that I can suggest is "It's forbidden to cancel the commonn factors between Numerator and denominator for Remainder and factors questions"

Cancelling common factors between numerator and denominator changes the numbers

e.g.

when 3 is divided by 2, the remainder is 1

But, when 6 is divided by 4, the remainder is 2

and, when 9 is divided by 6, the remainder is 3

whereas (3/2) = (6/4) = (9/6)
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Re: When the number 777 is divided by the integer N, the remaind  [#permalink]

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07 May 2018, 09:54
mainhoon wrote:
When the number 777 is divided by the integer N, the remainder is 77. How many integer possibilities are there for N?

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

We can create the equation:

777/N = Q + 77/N

When N = 700, the remainder is 77.

Thus, all factors of 700 that are greater than 77, will also leave a remainder of 77 when divided into 777.

Breaking 700 into primes, we have:

700 = 100 x 7 = 2^2 x 5^2 x 7^1

So factors of 700 that are greater than 77 are:

100, 7 x 25 = 175, 7 x 25 x 2 = 350, 7 x 4 x 5 = 140, and lastly, 700.

So there are 5 possibilities of N.

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Re: When the number 777 is divided by the integer N, the remaind &nbs [#permalink] 07 May 2018, 09:54

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