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aselfmademan
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What is greatest positive integer n such that 2^n is a factor of 12^10 Updated on: 31 Dec 2025, 03:17
Originally posted by aselfmademan on 27 Oct 2011, 00:06.
Last edited by Bunuel on 31 Dec 2025, 03:17, edited 1 time in total.
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82% (00:51) correct 18% (01:13) wrong based on 753 sessions

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What is greatest positive integer n such that 2^n is a factor of 12^10?

A. 10
B. 12
C. 16
D. 20
E. 60
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What is greatest positive integer n such that 2^n is a factor of 12^10 27 Oct 2011, 00:32
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aselfmademan
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...
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The given number is 12^10
=(2*2*3)^10
=(2^20)*(3^10)

So the greatest possible value for n such that 2^n can be factor of given number is 20.

Posted from my mobile device
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What is greatest positive integer n such that 2^n is a factor of 12^10 27 Oct 2011, 05:02
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aselfmademan
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...
Show more

\(12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}\)
The greatest value of n such that \(2^n\) is a factor of \(12^{10}\) is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that \(2^n\) is a factor of 12!
Try this one.
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What is greatest positive integer n such that 2^n is a factor of 12^10 27 Oct 2011, 08:03
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aselfmademan
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...

\(12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}\)
The greatest value of n such that \(2^n\) is a factor of \(12^{10}\) is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that \(2^n\) is a factor of 12!
Try this one.
Show more

Thank you very much.......... :-D I am very weak in this type of PS math :(
Could you please explain 12! math you have given ?
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What is greatest positive integer n such that 2^n is a factor of 12^10 27 Oct 2011, 20:32
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aselfmademan
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...

\(12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}\)
The greatest value of n such that \(2^n\) is a factor of \(12^{10}\) is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that \(2^n\) is a factor of 12!
Try this one.
Show more


n = 10

I just counted the number of 2s till 12 since the 12! is multiplication of all numbers till 12


Do you have any faster method which can be used for bigger factorials?
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What is greatest positive integer n such that 2^n is a factor of 12^10 Updated on: 11 Oct 2022, 00:49
Originally posted by KarishmaB on 27 Oct 2011, 20:39.
Last edited by KarishmaB on 11 Oct 2022, 00:49, edited 1 time in total.
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What is greatest positive integer n such that 2^n is a factor of 12^10 07 Mar 2016, 09:36
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aselfmademan
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60
Show more

Similar question to practice: what-is-the-largest-integer-n-such-that-2-n-is-a-factor-of-158297.html
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What is greatest positive integer n such that 2^n is a factor of 12^10 14 Mar 2016, 05:57
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Nice One.
Here breaking down 12^10 => 2^20 *3^10
so 20 is our answer
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What is greatest positive integer n such that 2^n is a factor of 12^10 02 Feb 2018, 11:28
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Hi All,

This question comes down to exponent rules and how to 'rewrite' a number raised to a power.

12 = (2)(2)(3)

12^2 = (2^2)(2^2)(3^2) = (2^4)(3^2)
12^3 = (2^3)(2^3)(3^3) = (2^6)(3^3)

Seeing this pattern, you should be able to rewrite 12^10...

12^10 = (2^10)(2^10)(3^10) = (2^20)(3^10)

So the largest 'power of 2' that is a factor of 12^10 is 20.

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D


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What is greatest positive integer n such that 2^n is a factor of 12^10 05 Oct 2020, 01:28
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Lets write \(12^{10} in the prime factors: (2 * 2 * 3)^{10}\)

=> \((2 ^2)^{10} * (3)^{10}\)

=> \((2)^{20} * (3)^{10}\)

The greatest possible value of n = 20

Answer D
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What is greatest positive integer n such that 2^n is a factor of 12^10 31 Dec 2025, 23:03
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