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What is the value of x if 823519 divided by x produces a remainder that is three times the remainder obtained by dividing 274658 by x and x is greater than one?
Wiki User
∙ 13y ago
226186081502
Sabryna Dooley
Wiki User
∙ 13y agoLet k be the whole number we are searching for.
Let 823519 divided by k be n, remainder 3r
and 274658 divided by k be m, remainder r
Then
823519 = n k + 3r and
274658 = m k + r
Multiply the second equation by three and subtract the first:
455 = (3m - n) k
So k is a factor of 455.
That means it is 1,5,7,13,35,65,91 or 455
I can write 823519 as 1809*455 + 424
Each time I divide this by one of the eight possibilities for k the 1809*455 part will
go exactly and not change the remainder. so I only need to look at the 424 part.
Listing the possibilities:
424 divided by 1 has a remainder of 0
424 divided by 5 has a remainder of 4
424 divided by 7 has a remainder of 4
424 divided by 13 has a remainder of 8
424 divided by 35 has a remainder of 179
424 divided by 65 has a remainder of 34
424 divided by 91 has a remainder of 60
424 divided by 455 has a remainder of 424
The 1 and 91 choices are the only ones which leave a remainder which is a multiple of 3
274658 divided by 91 has a remainder of 20.
Therefore the answer is 91!
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