document.write( "Question 1108922: The number 111...111000...000, made of 39 ones followed by 93 zeros, is NOT divisible by
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Algebra.Com's Answer #723941 by ikleyn(53763) $\"\"$ $\"About$

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document.write( "a)  Obviously, the given number is divisible by 4 and by 3, so it is divisible by 12.\r\n" );
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document.write( "    For divisibility on 3, apply the divisibility by 3 rule:\r\n" );
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document.write( "            The number is divisible by 3 if and only if the sum of its digits is divisible by 3.\r\n" );
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document.write( "            See the lesson Divisibility by 3 rule in this site.\r\n" );
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document.write( "    It is the case, since the sum of the digits 39 is divisible by 3, the number is divisible by 3.\r\n" );
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document.write( "b)  The number 10000 is divisible by 16 (direct check !),\r\n" );
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document.write( "    Hence, the given number is divisible by 16.\r\n" );
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document.write( "c)  The given number IS NOT divisible by 11.\r\n" );
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document.write( "    For divisibility on 11, apply the divisibility by 11 rule:\r\n" );
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document.write( "            The number is divisible by 1 if and only if the alternate sum of its digits is divisible by 11.\r\n" );
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document.write( "            See the lesson Divisibility by 11 rule in this site.\r\n" );
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document.write( "    It is the case, the alternate sum of the digits is 1 (one). Since it is not divisible by 11, the number itself IS NOT divisible by 11.\r\n" );
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document.write( "    Since the number is not divisible by 11, it IS NOT divisible by 22.\r\n" );
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document.write( "d)  Regarding the number 37, it is useful to know that 111 = 37*3.\r\n" );
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document.write( "    It follows from this fact that the given number is divisible by 37.\r\n" );
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document.write( "e)  625 = 5^4.   10^4 = 10000 is divisible by 5^.\r\n" );
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document.write( "    So the given number is divisible by 625.\r\n" );
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\n" ); document.write( "\n" ); document.write( "From this considerations, the only answer to the problem's question is the number 22.\r
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