Question
Find the highest power of 360 which divides 520!
CAT 2021
Solution
Correct option is
(C)
Explanatory Answer
As we know, 360 = 5*2*2*2*3*3
5 , 3*3 ,2*2*2, the one which appears the least number of times in will be the answer. among these
Number of 5’s in 520! = 520/5 + 520/5*5 + 520/5*5*5....
104+20+4 = 128
In order to find the number of 3^2s in 520! , we first need to find the number of 3s in 520!
Number of 3’s in 520! = 520/3 + 520/3*3 + 520/3*3*3....
= 173 +57+ 19 + 6 +2 = 257
Number of 3^2 , we get , 257/2 =128
In order to find the number of 2^3s in 520! , we first need to find the number of 2s in 520!
Number of 2’s in 520! = 520/2 + 520/2*2 + 520/2*2*2....
260 + 130 +65 +32 +16 + 8 + 4+2 +1 = 518
Number of 2^3 , we get , 518/3 = 172
so , least is 128hence , c is the correct option
