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What is the maximum value of m such that 7^m divides into 14
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14 Apr 2018, 02:29
14 Apr 2018, 02:29
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85% (00:40) correct
14% (01:08) wrong based on 61 sessions
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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
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Re: What is the maximum value of m such that 7^m divides into 14
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16 Apr 2018, 22:01
16 Apr 2018, 22:01
1
\(14!\) 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 \(m = 2\)
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 \(m = 2\)
Re: What is the maximum value of m such that 7^m divides into 14
[#permalink]
08 May 2018, 05:41
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 \(m = 2\)
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..
Please explain.
