Question
Quantitative Aptitude Question on Number Systems
Let X=11×12×13×_____×75. Suppose ‘X’ is divisible by 102k (where ‘k’ is a natural no.). Find the maximum value of ‘k’.
A
7.5
B
16
C
7
D
8
Answer
8
Explanation
Solution
10 = 2×5
Clearly in the prime factorization of ‘X’, (no. of factor ‘2’)>(no. of factor ‘5’).
⇒ No. of factor ‘5’ = (15-3+1) +3=16 [last ‘3’ is from terms having 25 as a factor i.e., 25, 50 and 75.]
⇒ k = 8
So, the correct option is (D): 8.