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Question
The highest power of 45 that will exactly divide 123! is
The highest power of 45 that will exactly divide 123! is
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Solution
The correct option is A 28
45=32×5. Hence, we need to count the number of 3^2's and 5's that can be made out of 123!.
Number of 3's = 41 + 13 + 4 + 1 = 59
Number of 5's =24 + 4 = 28
The required answer is the lower of the two (viz. 28 and 59)Hence, option (a) 28 is correct.
45=32×5. Hence, we need to count the number of 3^2's and 5's that can be made out of 123!.
Number of 3's = 41 + 13 + 4 + 1 = 59
Number of 5's =24 + 4 = 28
The required answer is the lower of the two (viz. 28 and 59)Hence, option (a) 28 is correct.
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