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I am having difficulties with a problem from my exercise sheet for a University exam.

The problem statement is as following:

When dividing a number by 12, 15 or 48 there will always be a remainder of 10. If the number is the least posible, how many divisors does the number have?

How would you solve that problem?

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    If by least possible you mean least positive, the number is obviously $10$, which has $4$ positive divisors. Note that in general the numbers in question are the numbers that have remainder $10$ on division by $240$.2011-12-21

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