(Q). (i). Find the total number of factors of 54000
(ii). Sum of all factors of 54000
(iii). Sum of all factors of 54000 that ends with 5.
Solution:-
5400 = 2⁴ × 3³ × 5³
(i).
∴ total number of factors = (4 + 1)(3 + 1)(3 + 1)
= 80 Answer
(ii)
Sum of all the factors =
= 31×40×312
= 386880 Answer
(iii).
its factor will end with 5 sonly when it is odd factor ⇒ all the factors of 3³ × 5³ will satisfy the condition. Hence sum of all the factors of 3³ × 5³ is given by
= 40×156
∴ Required answer = 6240 Answer