What is the Remainder?

Number Theory Level 2

If a number is divided by 285, the remainder left is 77. If this same number is divided by 57, what is the remainder left?


The answer is 20.

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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4 solutions

285+77=362 now divide this num by 57 and u get 20 as remainder! simpli

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Panya Chunnanonda
Jul 25, 2014

N= (285* i)+ 77,...i= integers but 285= 57* 5 so N= (57* 5* i)+ 77 when divided N by 57=((57* 5* i)/ 57)+ (77/ 57) and 77/ 57= 1+ 20 so remainder= 20

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Md Yusuf
Jul 19, 2014

(285 , 57 ) = 0, so answer is (77 , 57 ) = 20

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Shivani Garg
Jun 9, 2014

285+77=362÷57=20

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21,945/285=77.......... so by my reckoning the answer should be 385 because 21,945/57=385.......... the question asks for the number that was divided by by 285 to then be divided by 57????

Lee Woods - 6 years, 11 months ago

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No, the question is asking for the remainder left after division. For example, 7 / 3 = 2 R 1. So the remainder in that case is one. In this case, X / 285 = k R 77. There are infinitely many numbers that when divided by 285 leave a remainder of 77, so X can be a multitude of values.

Seth Lovelace - 6 years, 11 months ago

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