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48

Every positive integer can be written uniquely as the product of primes.

So, a = p1^a1 x p2^a2. .. where p1, p2 … are primes, and a1, a2. .. are positive integers.

Also, that being the case, there are (a1+1)(a2+1)… factors.

Using this backwards, you want a number with exactly 10 factors. 10=2×5 = (1+1)(4+1)

The smallest value with exactly 10 factors is therefore 2^4 * 3^1 = 16 * 3 = 48

So your answer is 48

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Anonymous

4y ago

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