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

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CEO
Joined: 21 Jan 2007
Posts: 2736

Kudos [?]: 1023 [0], given: 4

Location: New York City
What is the largest value of N such that 98^98 is divisible [#permalink]

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19 Nov 2007, 06:20
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What is the largest value of N such that 98^98 is divisible by 7^N?

98
105
148
164
196

Kudos [?]: 1023 [0], given: 4

Director
Joined: 30 Nov 2006
Posts: 591

Kudos [?]: 307 [0], given: 0

Location: Kuwait

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19 Nov 2007, 06:29
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

Kudos [?]: 307 [0], given: 0

VP
Joined: 10 Jun 2007
Posts: 1436

Kudos [?]: 330 [0], given: 0

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19 Nov 2007, 06:59
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

Kudos [?]: 330 [0], given: 0

SVP
Joined: 21 Jul 2006
Posts: 1513

Kudos [?]: 978 [0], given: 1

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19 Nov 2007, 07:33
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

hope it helps!

Kudos [?]: 978 [0], given: 1

19 Nov 2007, 07:33
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