Question:
Let X=11×12×13×_____×75. Suppose ‘X’ is divisible by 102k (where ‘k’ is a natural no.). Find the maximum value of ‘k’.
Let X=11×12×13×_____×75. Suppose ‘X’ is divisible by 102k (where ‘k’ is a natural no.). Find the maximum value of ‘k’.
Updated On: Aug 31, 2024
- 7.5
- 16
- 7
- 8
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The Correct Option is D
Solution and Explanation
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.
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.
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