document.write( "Question 1023806: What is the least positive integer n such that n! is divisible by 1000?\r
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Algebra.Com's Answer #639301 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1000 = 5*5*5*2*2*2\r\n" );
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document.write( "To have a factorial divisible by 1000, it must have 3 factors of 5\r\n" );
document.write( "and 3 factors of 2.\r\n" );
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document.write( "Every other integer has a factor of 2 so there are plenty of those,\r\n" );
document.write( "so we must make sure that we have 3 factors of 5 somewhere in the\r\n" );
document.write( "products.  Let's start buiding our factorial\r\n" );
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document.write( "1*2*3*4*5  <-- that only has 1 factor of 5  \r\n" );
document.write( "(It already has 3 factors of 2)\r\n" );
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document.write( "So we keep putting on more factors:\r\n" );
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document.write( "1*2*3*4*5*6*7*8*9*10  <-- That only has 2 factors of 5\r\n" );
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document.write( "So we keep going once more:\r\n" );
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document.write( "1*2*3*4*5*6*7*8*9*10*11*12*13*14*15  <-- that's it!\r\n" );
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document.write( "That's 15!. It is the smallest factorial that is divisible by 1000.\r\n" );
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document.write( "Notice that 14! = 87178291200 won't do.\r\n" );
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document.write( "It only has two 0's on the end, so it's only divisible\r\n" );
document.write( "by 100. But\r\n" );
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document.write( "15! = 1307674368000\r\n" );
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document.write( "is the smallest factorial that has 3 0's on the end, which\r\n" );
document.write( "a number must have to be divisible by 1000.\r\n" );
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document.write( "Answer: 15! = 1307674368000\r\n" );
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document.write( "Edwin
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