SOLUTION: What is the greatest number of 5 digits which when divided by 16, 24, 30 and 36, 10 will remainder in each case?

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Question 982672: What is the greatest number of 5 digits which when divided by 16, 24, 30 and 36, 10 will remainder in each case?
Answer by ikleyn(52814) About Me  (Show Source):
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Let  x  be the unknown number.
Then  x-10  is divisible by  16,  24,  30 and  36, according to the condition.

It implies that  x-10  is divisible by  2%5E4,  5  and  9.
Hence,  x-10  is divisible by  16*5*9 = 720.

The greatest  5-digits number divided by  720  is  99360  (it is easy to check).
It means that  x-10 = 99360.
Hence,  x = 99370.