document.write( "Question 1035190: Suppose that p, q and r are distinct prime integers such that the product N = pq × qr × rp has a units digit of zero. What is the greatest number of consecutive zeros that can appear to the right of the last nonzero digit of N? \n" ); document.write( "
Algebra.Com's Answer #649845 by Edwin McCravy(20063)\"\" \"About 
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document.write( "There can only be 2 zeros on the end.  Here's why.\r\n" );
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document.write( "The only way to get a zero on the end is to multiply by 10.\r\n" );
document.write( "10 has prime factors 2 and 5.  With N = pq × qr × rp, there \r\n" );
document.write( "are two factors p, two factors q, and two factors r.  So one\r\n" );
document.write( "pair of like factors must be 2's and another pair 5's.  \r\n" );
document.write( "Regardless of what the third prime factor is, we can have 00 \r\n" );
document.write( "on the end only if we have a factor of 100 = 2×2×5×5. The \r\n" );
document.write( "smallest number that would have two 0's on the end is\r\n" );
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document.write( "N = pq × qr × rp = (2×3) × (3×5) × (5×2) = 900.\r\n" );
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document.write( "All such integers are of the form (2×3) × (3×r) × (r×2) where \r\n" );
document.write( "r is any prime larger than 3.  No factor of 1000 is possible,\r\n" );
document.write( "for that would take a product of three 2's and three 5's.\r\n" );
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document.write( "Edwin
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