document.write( "Question 550232: Find the greatest power of 98,which can divide 99! -98!.answer choices 10,9,8,14. \n" ); document.write( "
Algebra.Com's Answer #358850 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%2899%21-98%21%29%2F%2898%5En%29\" =\r\n" );
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document.write( "\"%2898%21%2899-1%29%29%2F%2898%5En%29\" =\r\n" );
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document.write( "\"%2898%21%2898%29%29%2F%2898%5En%29\" =\r\n" );
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document.write( "\"98%21%2F%28%282%2A7%2A7%29%5En%29\" =\r\n" );
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document.write( "\"98%21%2F%28++2%5En%2A7%5En%2A7%5En++%29\" =\r\n" );
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document.write( "\"98%21%2F%28++2%5En%2A7%5E%282n%29++%29\" =\r\n" );
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document.write( "The denominator must cancel entirely into the numerator.  If we have enough\r\n" );
document.write( "factors which are multiples of 7's in the denominator to cancel entirely into\r\n" );
document.write( "the multiples of 7's which are factors of the numerator, then we will\r\n" );
document.write( "automatically have enough factors of multiples of 2 since there are fewer\r\n" );
document.write( "multiples of 2 in the denominator than multiples of 7 and there are 48 even\r\n" );
document.write( "factors in the top, so we only need be sure there are as many factors which are\r\n" );
document.write( "multiples of 7 in the denominator to cancel into the 16 multiples of 7 in the\r\n" );
document.write( "numerator.  How did I know there were 16 multiples of 7 which are factors of\r\n" );
document.write( "the numerator?  Here's how I knew. The integers from 1 to 98, inclusive are\r\n" );
document.write( "factors of the numerator of 98!, there are 14 which are multiples of 7.  There\r\n" );
document.write( "are 98÷7 or 14 multiples of 7.  These are:\r\n" );
document.write( "7,14,21,28,35,42,49,56,63,70,77,84,91,98.  Each of those has 7 as a factor\r\n" );
document.write( "once, except 49 and 98 which each have a factor of 7 twice.  So that makes 16\r\n" );
document.write( "factors of 7 in the numerator. \r\n" );
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document.write( "So the 2n 7's in the bottom must cancel completely into the the 16 multiples of\r\n" );
document.write( "7 in the top.  So\r\n" );
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document.write( "    2n ≤ 16\r\n" );
document.write( "     n ≤ 8\r\n" );
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document.write( "So 8 is the biggest possible value of n.\r\n" );
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document.write( "Edwin
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