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a boy with a collection of marbles realizes that if he makes a group of 5 or 6 marbles at a time there are always 2 marbles left can you explain why the boy cannot have prime number of marbles

a boy with a collection of marbles realizes that if he makes a group of 5 or 6 marbles at a time there are always 2 marbles left can you explain why the boy cannot have prime number of marbles
 

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1 Answers

Ashwin
41 Points
8 years ago
Hi,
 
let n be any number 
therefore, Accourding to question ,
number of marbles is 5n+2 or 6m+2 ,
=> marbles are a multiple of 5 or 6 plus 2 marbles.
From this we can conclude that the number of marbles must be a multiple 5x6 or 30  plus even number 2.
Hence number of marbles cannot be a prime number. 
 
Regards,
Ashwin

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