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

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Manager
Joined: 04 Jul 2017
Posts: 61
Location: India
Concentration: Marketing, General Management
GPA: 1
WE: Analyst (Consulting)
What is the largest value of integer n such that 98^98 is divisible by  [#permalink]

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Updated on: 27 Sep 2017, 10:29
4
00:00

Difficulty:

5% (low)

Question Stats:

85% (00:50) correct 15% (00:10) wrong based on 53 sessions

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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

Do not have the OA.
The question is from gmatclub itself and appeared in QOTD. However, the discussion link is taking us to another question.

Originally posted by aashishagarwal2 on 27 Sep 2017, 09:53.
Last edited by Bunuel on 27 Sep 2017, 10:29, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Senior Manager
Joined: 19 Apr 2016
Posts: 274
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
Re: What is the largest value of integer n such that 98^98 is divisible by  [#permalink]

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27 Sep 2017, 10:09
1
98=2*7*7
98^98 =2^98 * (7^2)^98 =2^98 * 7^196

So n =196
Hence Option E is correct

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Math Expert
Joined: 02 Sep 2009
Posts: 47946
Re: What is the largest value of integer n such that 98^98 is divisible by  [#permalink]

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27 Sep 2017, 10:29
1
aashishagarwal2 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

Do not have the OA.
The question is from gmatclub itself and appeared in QOTD. However, the discussion link is taking us to another question.

$$98^{98}=(2*49)^{98}=(2*7^2)^{98}=2^{98}*7^{196}$$. Therefore the largest value of integer $$n$$ such that $$2^{98}*7^{196}$$ is sidvisible by $$7^n$$ is 196.

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Re: What is the largest value of integer n such that 98^98 is divisible by &nbs [#permalink] 27 Sep 2017, 10:29
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# What is the largest value of integer n such that 98^98 is divisible by

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