Melody

Deleted. Diagram was wrong.

It always helps if you read and inprete the question properly.

Thanks Builderboi.

I have only half checked what you have done it but it looks like a really nice solution.   

sum of roots is 121/24

\(a+b+c=\frac{121}{24}\\ ab+ac+bc=\frac{87}{24}=\frac{29}{8}\\ abc=\frac{8}{24}=\frac{1}{3}\)

\(\log_3(a)+\log_3(b)+\log_3(c)\\ =log_3(abc)\\ =log_3(\frac{1}{3})\\ =log_3(3^{-1})\\ =-1log_3(3)\\ =-1\)

If I understand the question correctly then the smallest 47 numbers will be

0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8, 9,9,10,10,11,11,12,12, ...... 22,22,23

average of 0,1,2, ... 22 =  [23/2(0+22) ]/23= 11

average of  0,1,2,3, ... 23  =  [24/2(0+23]/24= 11.5

avverage of 11 and  11.5  =  11.25

You are very welcome.  

or maybe you meant that the factors have to be between 30 and 140 ??    [The meaning of the question is not clear]

1 is a factor for all integers ....  

2210269 = = 31*37*41*47 

the only other factors are 1 and 2210269

If a number is the multiple of 2 prime numbers it will have exactly 4 factors

eg

7*11=77    factors are   1,7,11,77

The fraction element of the calc has never worked well.  I suggest you use a different calc for fractions.

I just answered a very similar question here;

Hint:

You cannot divide by zero.  So none of the denominators can be equal to 0.

Thanks inhuman calculator, you have given a great answer          [You should give yourself a point  ]

I'll just add a little

-(3)^2 can be expanded to   -1*(3)^2    now it should be easy to see that the answer is -1*9 = -9

however

(-3)^2   is   -3 * -3  =  +9