Question

Find the highest power of 360 which divides 520!​

CAT 2021

A
192
CORRECT ANSWER WRONG ANSWER
B
232
CORRECT ANSWERWRONG ANSWER
C
128
CORRECT ANSWER WRONG ANSWER
D
240
CORRECT ANSWER WRONG ANSWER
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 128

hence , c is the correct option