document.write( "Question 445801: what is the prime factorization of 304 \n" ); document.write( "
Algebra.Com's Answer #307009 by Edwin McCravy(20056) $\"\"$ $\"About$
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document.write( "what is the prime factorization of 304\r\n" );
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document.write( "I noticed that 304's last digit is 4. \r\n" );
document.write( "Then I noticed that if you have a whole number of things \r\n" );
document.write( "and that whole number ends in either a 2,4,6,8, or 0 then\r\n" );
document.write( "you can split your things up into two equal piles or groups.  \r\n" );
document.write( "So we call such numbers as that \"even\" numbers. But if you have \r\n" );
document.write( "an odd number of things to divide up, you'll have to cut one \r\n" );
document.write( "thing in two to do it.\r\n" );
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document.write( "What we want to do is to keep dividing until we can divide no \r\n" );
document.write( "more.  But we never divide a number by itself or by 1. That's \r\n" );
document.write( "because if we divide a number by itself we get 1, and if we \r\n" );
document.write( "divide a number by 1 we get itself, i.e., the same number back.  \r\n" );
document.write( "So we're getting nowhere, so we avoid that in our division.  1 \r\n" );
document.write( "is not considered a prime. But it was once considered prime.  \r\n" );
document.write( "In the old Chemical Rubber Co. mathematical tables, 1 was listed \r\n" );
document.write( "in the table of primes.  There is a reason why mathematicians \r\n" );
document.write( "stopped considering 1 to be prime, but I won't go there. \r\n" );
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document.write( "Anyway,\r\n" );
document.write( "Hey, 304 ends in a 2\r\n" );
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document.write( "So I'll divide it by 2\r\n" );
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document.write( "I get 152\r\n" );
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document.write( "So 304 = 2*152\r\n" );
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document.write( "Hey, 152 ends in a 2\r\n" );
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document.write( "So I'll divide it by 2\r\n" );
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document.write( "I get 76\r\n" );
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document.write( "So 304 = 2*2*76\r\n" );
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document.write( "Hey, 76 ends in a 6\r\n" );
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document.write( "So I'll divide it by 2\r\n" );
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document.write( "I get 38\r\n" );
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document.write( "So 304 = 2*2*2*38\r\n" );
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document.write( "Hey, 38 ends in a 2\r\n" );
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document.write( "So I'll divide it by 2\r\n" );
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document.write( "I get 19\r\n" );
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document.write( "So 304 = 2*2*2*2*19\r\n" );
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document.write( "Oh! Oh! We've come to a halt. We can't divide 19 by anything except 1.\r\n" );
document.write( "Not only is 19 odd, but it's also prime. \r\n" );
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document.write( "So that's the factorization of 304 into prime numbers:\r\n" );
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document.write( "   304 = 2*2*2*2*19\r\n" );
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document.write( "So 304 = 2*2*2*2*19\r\n" );
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document.write( "And now we're stuck. This roller coaster came to a halt.\r\n" );
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document.write( "That's it:\r\n" );
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document.write( "2*2*2*2*19 is the prime factorization of 304.\r\n" );
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document.write( "Edwin
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