document.write( "Question 1204671: 36, 48, 60 find the largest common factor of the numbers \n" ); document.write( "

Algebra.Com's Answer #841087 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Here is one elementary way of finding the greatest common factor, by finding the prime factorization of each number.

\n" ); document.write( "36 = 2*2*3*3
\n" ); document.write( "48 = 2*2*2*2*3
\n" ); document.write( "60 = 2*2*3*5

\n" ); document.write( "The greatest common factor is the product of all the primes that are common to all three numbers: 2*2*3 = 12.

\n" ); document.write( "And here is one of many other ways of finding the greatest common factor.

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document.write( "       36   48   60\r\n" );
document.write( "     |\r\n" );
document.write( "     +--------------\r\n" );
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document.write( "Find any factor common to all three numbers; write that number on the left, and remove that common factor from each of the three numbers:\r\n" );
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document.write( "       36   48   60\r\n" );
document.write( "  3  | 12   16   20\r\n" );
document.write( "     +--------------\r\n" );
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document.write( "Continue doing that until there are no more common factors in the three remaining numbers:\r\n" );
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document.write( "       36   48   60\r\n" );
document.write( "  3  | 12   16   20\r\n" );
document.write( "  2  |  6    8   10\r\n" );
document.write( "  2  |  3    4    5\r\n" );
document.write( "     +--------------\r\n" );
document.write( "\r\n" );
document.write( "The greatest common factor of the three numbers is the product of the common factors you have removed: 3*2*2 = 12.\r\n" );
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document.write( "Note this process also finds the least common multiple of the three numbers.  It is the greatest common factor, times the numbers that remain: (3*2*2)*(3*4*5) = 12*60 = 720.

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