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14 Jan 2026, 22:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
54% (01:57) correct
46%
(01:40)
wrong
based on 145
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What is the highest integer k for which 135^k perfectly divides 200! ?
A. 97
B. 49
C. 40
D. 32
E. 1
A. 97
B. 49
C. 40
D. 32
E. 1
15 Jan 2026, 00:43
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ExpertsGlobal5
The highest power of k in 135^k that perfectly divides 200!
135 on prime factorisation gives 3^3* 5
We have to look for powers of 3, since 3^3 occurs at a much lower repetition than 5.
200! On successive division by 3 = 66+22+7+2 = 97
3^97 can be represented as 3^(3*32) * 3.
Thus, the highest power of 135^K in 200! is 32.
Option D
