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What is the largest value of N such that 98^98 is divisible

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CEO
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What is the largest value of N such that 98^98 is divisible [#permalink] New post 19 Nov 2007, 05:20
What is the largest value of N such that 98^98 is divisible by 7^N?

98
105
148
164
196
Director
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 [#permalink] New post 19 Nov 2007, 05:29
No way I would see a question in the GMAT this hard; If I do, I would guess with an uneducated guess and not spend more than 1 second on it.

Sorry, But i don't think this is a gmat level question. i wish i could help
VP
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Re: 98^98 [#permalink] New post 19 Nov 2007, 05:59
bmwhype2 wrote:
What is the largest value of N such that 98^98 is divisible by 7^N?

98
105
148
164
196


98 = 2*7*7
98^98 = (2*7*7)^98 = 2^98 * 7^(2*98) = 2^98 * 7^196

N = 196
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 [#permalink] New post 19 Nov 2007, 06:33
With this question, you are basically looking for the maximum powers of 7 that will yield either equal to or less than 98. When you look at 7^2, you get a value of 49. And 7^3 is 343, therefore, we are not interested in the 7^3 because its value is much larger than 98. Therefore:

98^98 / 7^N = (49^98 * 2^98) / 7^N Note: 49*2 is 98!!!

then: (7^2^98) * (2^98) / 7^N Note: multiply the ^2 by ^98

therefore: 7^ (2 * 98) = 7^ 196

This is our answer: 196

hope it helps!
  [#permalink] 19 Nov 2007, 06:33
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What is the largest value of N such that 98^98 is divisible

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