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What is the largest value of integer n such that

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by VJesus12 » Sun Apr 14, 2019 10:22 am

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

A. 98
B. 105
C. 148
D. 164
E. 196

[spoiler]OA=E[/spoiler]

Source: GMAT Club Tests
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by Brent@GMATPrepNow » Sun Apr 14, 2019 3:32 pm
VJesus12 wrote:What is the largest value of integer n such that 98^98 is divisible by 7^n?

A. 98
B. 105
C. 148
D. 164
E. 196

[spoiler]OA=E[/spoiler]

Source: GMAT Club Tests
98 = (2)(7)(7) = (2^1)(7^2)

So, 98^98 = [(2^1)(7^2)]^98
= (2^98)(7^196)

What is the largest value of integer n such that 98^98 is divisible by 7^n?
Since 98^98 = (2^98)(7^196), the largest value of n is 196

Answer: E

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Wed Apr 17, 2019 5:47 pm
VJesus12 wrote:What is the largest value of integer n such that 98^98 is divisible by 7^n?

A. 98
B. 105
C. 148
D. 164
E. 196

[spoiler]OA=E[/spoiler]

Source: GMAT Club Tests
Since 98^98 = (7^2 x 2^1)^98 = 7^196 x 2^98, the largest value of n is 196.

Answer: E

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