document.write( "Question 117738: Please help. Thank you
\n" ); document.write( "Choose the correct greatest common factor of 105 and 147
\n" ); document.write( "a) 21 b) 15 c) 63 d) 20 \n" ); document.write( "

Algebra.Com's Answer #85737 by MathLover1(20849) $\"\"$ $\"About$

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The $\"greatest\"$ $\"+common\"$ $\"+factor\"$ of two or more whole numbers is the $\"largest\"$ $\"+whole\"$ $\"+number\"$ that $\"divides\"$ $\"+evenly\"$ into each of the numbers.
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\n" ); document.write( "\n" ); document.write( "There are $\"two\"$ $\"ways\"$ to find the greatest common factor. \r
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\n" ); document.write( "\n" ); document.write( "The $\"first\"$ $\"+method\"$ is to list all of the factors of each number, then list the $\"common\"$ $\"+factors\"$ and choose the $\"largest\"$ $\"+one\"$ . \r
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\n" ); document.write( "\n" ); document.write( "the $\"GCF\"$ of $\"105\"$ and $\"147\"$ :\r
\n" ); document.write( "\n" ); document.write( "the factors of $\"105\"$ are $\"1\"$ , $\"+3\"$ , $\"5\"$ , $\"7\"$ , $\"15\"$ , $\"21\"$ , $\"35\"$ and $\"105\"$ \r
\n" ); document.write( "\n" ); document.write( "thefactors of $\"147\"$ are $\"1\"$ , $\"++3\"$ , $\"+7\"$ , $\"+21\"$ , $\"+49\"$ and $\"147\"$ \r
\n" ); document.write( "\n" ); document.write( "the $\"common\"$ factors of $\"105\"$ and $\"147\"$ are $\"1\"$ , $\"3\"$ , $\"+7\"$ , $\"+21\"$ \r
\n" ); document.write( "\n" ); document.write( "Although the numbers in bold are all common factors of both $\"105\"$ and $\"147\"$ , $\"21\"$ is the greatest common factor.\r
\n" ); document.write( "\n" ); document.write( "The $\"second\"$ $\"+method\"$ for finding the greatest common factor is:\r
\n" ); document.write( "\n" ); document.write( " to list the $\"+prime+\"$ $\"factors\"$ , then $\"multiply\"$ the $\"common\"$ $\"+prime\"$ $\"+factors\"$
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\n" ); document.write( "The prime factorization of $\"105\"$ and $\"147\"$ is:
\n" ); document.write( " $\"105+=3%2A5%2A7\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"147=3%2A7%2A7\"$ \r
\n" ); document.write( "\n" ); document.write( "Notice that the prime factorizations of $\"105\"$ and $\"147\"$ both have one $\"+3\"$ and one $\"7\"$ in common. \r
\n" ); document.write( "\n" ); document.write( "So, we simply $\"multiply\"$ these common prime factors to find the greatest common factor:
\n" ); document.write( " $\"3+%2A7=+21\"$
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\n" ); document.write( "so, correct answer is: a) $\"21+\"$
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