document.write( "Question 949378: 1!+2!+3!+....+100! divide by 5? \n" ); document.write( "

Algebra.Com's Answer #579611 by KMST(5328) $\"\"$ $\"About$

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$\"5%21=1%2A2%2A3%2A4%2A5\"$ is divisible by $\"5\"$ . In other words,
\n" ); document.write( " $\"5%21%2F5=1%2A2%2A3%2A4%2A5%2F5=1%2A2%2A3%2A4=4%21=24\"$ is an integer.
\n" ); document.write( "The same is true about the factorials of every number greater than $\"5\"$ .
\n" ); document.write( "In other words, if $\"k\"$ is a positive integer and $\"k%3E5\"$ ,
\n" ); document.write( " $\"k%21%2F5\"$ is a positive integer.
\n" ); document.write( "So, in the case of

,
\n" ); document.write( "we know that all the terms except the first term are positive integers.
\n" ); document.write( "What about that first $\"%281%21%2B2%21%2B3%21%2B4%21%29%2F5\"$ term?
\n" ); document.write( "

\n" ); document.write( "is not an integer.
\n" ); document.write( "When you divide $\"1%21%2B2%21%2B3%21%2B4%21\"$ by $\"5\"$ you get
\n" ); document.write( "an integer quotient, $\"6\"$ , and a remainder, $\"3\"$ .
\n" ); document.write( "The same happens when you divide $\"1%21%2B2%21%2B3%21%2B%22....%22%2B100%21\"$ by $\"5\"$ :
\n" ); document.write( "you get an integer quotient, and $\"3\"$ for a remainder. \n" ); document.write( "

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