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The required number is 48; its factors are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

When a number is expressed in its prime factorisation in power format, the number of factors of the number is the product of the power of each prime plus one, ie if n = p1^r1 × p2^r2 × ... × pm^rm, then the number of factors is given by Π(ri + 1) for i = 1, 2, ..., m.

10 can be factorised as 1 × 10 or 2 × 5.

In the first case, it would require a prime to the power 9; the smallest prime is 2 and 2^9 = 512 which exceeds 50.

Thus the only possibility is 2 × 5 which means the number is made up of 2 primes, one to the power 1 and the other to the power 4. The solution is likely to contain the two smallest primes which are 2 and 3, but which way to assign the powers. 3^4 = 81 which exceeds 50, so the choice left is 2^4 × 3^1 = 48 - the required solution.

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9y ago

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i dont know the ans

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Anonymous

4y ago
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1234578

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Anonymous

4y ago
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Q: What number is less than 50 that has 10 factors?
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