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The remainders when three positive integers are divided by 5 are 1, 2, and 3. Find the remainder when their product is divided by 5.       

 Aug 17, 2023
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Let the integers be

 

5m + 1 , 5n + 2 and  5p + 3

 

Their product  =    ( 5m + 1) ( 5n + 2) ( 5p + 3)  = 

 

(25mn + 5n + 10m + 2) ( 5p + 3)  =

 

125 pmn + 25pn + 50pm + 10p  + 75mn + 15n + 30m + 6

 

Each of the first  terms   divided by 5 will yield and integer and these added together  will also yield an integer

 

Only the last term  divided by 5  will yield a remainder of 1

 

cool cool cool

 Aug 17, 2023

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