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# What is the maximum value of m such that 7^m divides into 14

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What is the maximum value of m such that 7^m divides into 14 [#permalink]  14 Apr 2018, 02:29
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Question Stats:

82% (00:40) correct 17% (01:18) wrong based on 28 sessions
What is the maximum value of m such that $$7^m$$ divides into $$14!$$ evenly?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
[Reveal] Spoiler: OA

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Re: What is the maximum value of m such that 7^m divides into 14 [#permalink]  16 Apr 2018, 22:01
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$$14!$$ can be written as $$14*13*12*11*10*9*8*7*6*5*4*3*2*1$$
Here we only need terms that are multiples of $$7$$ so we have $$14$$ and$$7$$.
$$14$$ can be rewritten as $$7 *2$$ hence in this factorial we have $$7^2 * a$$ ; where a is all the other remaining numbers multiplied together
Hence in the expression $$7^m$$ m can acquire the maximum value of $$2$$
option B

Another approach is to divide the factorial number by the number in question whose power is to be raised
Therefore $$\frac{14}{7} = 2$$
$$2$$ cannot be further divided by $$7$$ hence $$m = 2$$
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Re: What is the maximum value of m such that 7^m divides into 14 [#permalink]  08 May 2018, 05:41
amorphous wrote:
$$14!$$ can be written as $$14*13*12*11*10*9*8*7*6*5*4*3*2*1$$
Here we only need terms that are multiples of $$7$$ so we have $$14$$ and$$7$$.
$$14$$ can be rewritten as $$7 *2$$ hence in this factorial we have $$7^2 * a$$ ; where a is all the other remaining numbers multiplied together
Hence in the expression $$7^m$$ m can acquire the maximum value of $$2$$
option B

Another approach is to divide the factorial number by the number in question whose power is to be raised
Therefore $$\frac{14}{7} = 2$$
$$2$$ cannot be further divided by $$7$$ hence $$m = 2$$

I am unable to understand the questions..I thought we need to find M , for which when 7 raised to M divides completely 14!.

but the explanation is focused upon find the value of m for which when 7 is raised it devides 14 complete .. it is a no brainer ..it has to be 2..

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Re: What is the maximum value of m such that 7^m divides into 14 [#permalink]  08 May 2018, 09:26
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wording for a question can be tricky. The question is asking how many times 7 can be raised within 14!.

GRE does not throw lengthy problems that takes up lots of time in solving. If your reasoning involves lots of computations probably you need to look at the problem from a different angle. In fact the use of calculator is to make sure that test is focused on testing concepts over tedious working on part of test-takers.
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Re: What is the maximum value of m such that 7^m divides into 14 [#permalink]  08 May 2018, 09:57
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Expert's post
Carcass wrote:
What is the maximum value of m such that $$7^m$$ divides into $$14!$$ evenly?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

This question needs some kind of information that restricts the value of m to integer values only.
Otherwise, there exists a non-integer value of m such that 7^m = 14!
To be more precise, 7^(12.946) ≈ 14!, which means 7^(12.946) is definitely a divisor of 14!

Cheers,
Brent
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Re: What is the maximum value of m such that 7^m divides into 14 [#permalink]  09 May 2018, 21:10
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amorphous wrote:
wording for a question can be tricky. The question is asking how many times 7 can be raised within 14!.

GRE does not throw lengthy problems that takes up lots of time in solving. If your reasoning involves lots of computations probably you need to look at the problem from a different angle. In fact the use of calculator is to make sure that test is focused on testing concepts over tedious working on part of test-takers.

I tend to focus more on calculations rather than concepts, before your comment I used to think the more faster and efficiently I can calculate the better it is. since it is maths ,calculation will be an important part of it but the reason you gave about the calculator used in the TEST is really insightful.

test is testing our concepts hmm

Thank you
Re: What is the maximum value of m such that 7^m divides into 14   [#permalink] 09 May 2018, 21:10
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