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# X is the product of integers from 1 to 8. If 2^m is a factor

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X is the product of integers from 1 to 8. If 2^m is a factor [#permalink]  26 Apr 2006, 02:36
X is the product of integers from 1 to 8. If 2^m is a factor of x, what is the greatest possible value of m?
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x = 1*2*3*4*5*6*7*8

when we take all 2's possible we get

2*4*2*8 = 2^7

m=7
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An alternate approach

One of the standard ways to find this out will be to successively divide 8 by 2 till you can divide no further and add the quotients.

In this case 8 divided by 2 quotient is 4
4 divided by 2 quotient is 2
2 divided by 2 quotient is 1
2 will not be able to divide 1 further.

Therefore, highest power of 2 that can divide factorial 8 i.e, 1*2*3*...8 will be the sum of the quotients 4 + 2 + 1 = 7
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