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Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]
19 Mar 2012, 22:47

3

This post received KUDOS

Expert's post

essarr wrote:

If 6^y is a factor of (10!)^2, What is the greatest possible value of y ?

A. 2 B. 4 C. 6 D. 8 E. 10

... I was hoping to get a better explanation, as I'm still confused about the explanation provided. Thanks!

6=2*3. Now, there will be obviously less 3's than 2's in (10!)^2, so maximum power of 3 will be limiting factor for maximum power of 6, which is y.

Finding the maximum powers of a prime number 3, in 10!: \frac{10}{3}+\frac{10}{3^2}=3+1=4 (take only quotients into account). So, we have that the maximum power of 3 in 10! is 4, thus maximum power of 3 in (10!)^2 will be 8: (3^4)^2=3^8. As discussed 8 is the maximum power of 6 as well.

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]
23 Mar 2012, 01:49

Expert's post

pappueshwar wrote:

hi bunuel,

i did nt understand how did u get 3's more than 2's in 10!.

i am of the view that 10! = 10*9*8*7*6*5*4*3*2*1

if we expand this we get = 2*5*3*3*2*2*2 *7 *3*2* 5* 2*2* 3* 2 *1

so there are 8 2's and 4 3's in the expansion above.

so how to interpret this and proceed

It's: "there will be obviously LESS 3's than 2's in (10!)^2, so maximum power of 3 will be limiting factor for maximum power of 6, which is y." _________________

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]
01 Oct 2012, 05:13

Factorial of 10 can be written as 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

or 2 x 5 x 3 x 3 x 2 x 2 x 2 x 7 x 2 x 3 x 5 x 2 x 2 x 3 x 2 x 1

So in 10 factorial we have 08 2's and 4 three's ... Square of 10 factorial will give us 16 2's and 8 three's

to get six we know that we would have to take one 2 and one three ..the maximum number of three's we can take is 8 therefore 8 different 6's can be formed therefore max possible value of y can be 6 ..

2 x 3 2 x 3 2 x 3 2 x 3 2 x 3 2 x 3 2 x 3 2 x 3

D.. _________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]
01 Oct 2012, 05:13

Factorial of 10 can be written as 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

or 2 x 5 x 3 x 3 x 2 x 2 x 2 x 7 x 2 x 3 x 5 x 2 x 2 x 3 x 2 x 1

So in 10 factorial we have 08 2's and 4 three's ... Square of 10 factorial will give us 16 2's and 8 three's

to get six we know that we would have to take one 2 and one three ..the maximum number of three's we can take is 8 therefore 8 different 6's can be formed therefore max possible value of y can be 8 ..

2 x 3 2 x 3 2 x 3 2 x 3 2 x 3 2 x 3 2 x 3 2 x 3

D.. _________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Re: If 6^y is a factor of (10!)^2, What is the greatest possible [#permalink]
09 Jul 2014, 05:52

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