Question

p=441*484*529*576*625 . The total number of factors of P is?

Answer 1

441 = 21 x 21 i.e. 21²

484 = 2 x 2 x 11 x 11 i.e. 2² × 11²

529 = 23 x 23 i.e. 23²

576 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 i.e. $2^{6}$× 3²

625 = 5 x 5 x 5 x 5 i.e. $5^{4}$

21² x 2² × 11² x 23² x $2^{6}$× 3² x $5^{4}$

or, $2^{8}$ x 3² x $5^{4}$ x 11² x 21² x 23²

No of divisors = 9 x 3 x 5 x 3 x 3 x 3 = 3645.

The total number of factors of P is 3645.