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As 2 is the smallest Prime number

the number less than 50 that has the most factors can't have more than 5 factors cause 2^5=32 and 2^6=64.

So we're searching for a number with at most 5 factors

As sqrt(50) = 7.07..., the biggest factor can't be more than 7

The problem is then find pi (prime numbers) such that p1p2p3p4p5<50 and pi are not necessary different and pi <=7

We already know that 25 will do

24x3 will also do

24x5 won't

24x7 won't

23x32 > 50

22x33 > 50

2x34 > 50

35 > 50

34 > 50

following the same calculations with powers of 5 or 7 shows that there are no more solution

The solutions are 25 and 24x3

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