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What is the largest number $k$ less than 1000 such that the remainder is 1 when $k$ is divided by each of 3, 4, 5, 6, and 7?

 Dec 24, 2020
 #1
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You can start from 999 and continue down until you found a number that meets the requirment. 999 wouldn't work because when divided by 3, there is no remander. I'm sure it will not take too long.

 Dec 24, 2020
 #2
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What is the largest number less than 1000 such that the remainder is 1 when is divided by each of 3, 4, 5, 6, and 7?  

 

My submission is 841.  I multiplied 4 x 5 x 6 x 7 and got 840 then added 1. 

 

I didn't multiply by 3 because that ends up over a 1000 and anyway the 6 took care of the 3. 

 Dec 24, 2020
edited by Guest  Dec 24, 2020

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