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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?



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number of marbles is 5n+2 or 6m+2 ,i.e., a multiple of 5 or 6 plus 2 marbles. Hence number of marbles must be a multiple 5x6 or 30  plus even number 2.
i.e., 30p+2=2(15p+1) is an even number.
Hence number of marbles cannot be a prime number, because it is an even number.
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