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The largest integer value of x such that 4x divides exactly into 10! is?

 May 29, 2018
 #1
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Since 10! =3,628,800 = 2^8 * 3^4 * 5^2 * 7.

But 2^8 =(2^2)^4 =4^4

 May 29, 2018
 #2
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10!= 1*2*3*4*5*6*7*8*9*10

 

= 2*3*2*2*5*2*3*7*2*2*2*9*2*5

= 2*2*2*2*2*2*2*2*3*5*3*7*9*5

=   4 *  4  *  4  *  4  *3*5*3*7*9*5

=        4^4              *3*5*3*7*9*5

 

So the highest value of x is 4

 May 30, 2018

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