Question

A positive integer "n" has 60 divisors and 7n has
80 divisors. what is the greatest integer k such 7^k
that divides
(a)0 (B) 1 (C)7 (D)-2​

Answer 1

Answer:

D. 2

Step-by-step explanation:

n=2^a*3^b*5^c*7^d………..

The number of divisors of n is

=(a+1)*(b+1)*(c+1)*(d+1)*……………=60

The number of divisors of 7n is

=(a+1)*(b+1)*(c+1)*(d+2)*……..=80

(d+1)/(d+2)=60/80

(d+1)/(d+2)=3/4

d=2

So greatest integer k is 2