Answer:
9
Step-by-step explanation:
it’s clear that a ,b and c are in geometric progression.
Then we have :
a
b = q×a
c = q²×a
also , b² = a×c
………………………
NOTE : b² and b have the same factors
also ,since b² = a×c then b and a×c
have the same number of factors.
_______________________________
Since c = q²×a then any factor of a is also a factor of c
Which means the number of factors of a×c
is equal to the number of factors of c.
Therefore b at most has the same number of factors as c.
Conclusion:
at most b has 9 factors.
……………………
As a side note :
You can take as example the numbers 3 , 30 , 300.
3 ——-> 1 factor
30 = 3×5×2 ——-> 3 factors
300 = 3 × 5² × 2² ——-> 3 factors
