Strategy 2: List Factors

To use this strategy, list all the possible factors for each expression and determine the common factors.

Example 2

Determine the GCF of «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#191919¨»20«/mn»«msup mathcolor=¨#191919¨»«mi mathcolor=¨#191919¨»p«/mi»«mn»2«/mn»«/msup»«msup mathcolor=¨#191919¨»«mi mathcolor=¨#191919¨»q«/mi»«mn»2«/mn»«/msup»«/math» and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#191919¨»45«/mn»«msup mathcolor=¨#191919¨»«mi mathcolor=¨#191919¨»p«/mi»«mn»3«/mn»«/msup»«msup mathcolor=¨#191919¨»«mi mathcolor=¨#191919¨»q«/mi»«mn»4«/mn»«/msup»«/math» .

List the factors of each monomial and identify the largest factors that appear in both lists. The product of these largest factors will be the GCF.

«math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#B94A48¨»20«/mn»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»p«/mi»«mn»2«/mn»«/msup»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»q«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#B94A48¨»:«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»1«/mn»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»2«/mn»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»4«/mn»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#1C82BA¨»5«/mn»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»10«/mn»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»20«/mn»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mi mathcolor=¨#B94A48¨»p«/mi»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«msup mathcolor=¨#1C82BA¨»«mi mathcolor=¨#1C82BA¨»p«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mi mathcolor=¨#B94A48¨»q«/mi»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«msup mathcolor=¨#1C82BA¨»«mi mathcolor=¨#1C82BA¨»q«/mi»«mn»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathcolor=¨#B94A48¨»45«/mn»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»p«/mi»«mn»3«/mn»«/msup»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»q«/mi»«mn»4«/mn»«/msup»«mo mathcolor=¨#B94A48¨»:«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»1«/mn»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»3«/mn»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#1C82BA¨»5«/mn»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»9«/mn»«mo mathcolor=¨#B94A48¨».«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»15«/mn»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»45«/mn»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mi mathcolor=¨#B94A48¨»p«/mi»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«msup mathcolor=¨#1C82BA¨»«mi mathcolor=¨#1C82BA¨»p«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»p«/mi»«mn»3«/mn»«/msup»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mi mathcolor=¨#B94A48¨»q«/mi»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«msup mathcolor=¨#1C82BA¨»«mi mathcolor=¨#1C82BA¨»q«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»q«/mi»«mn»3«/mn»«/msup»«mo mathcolor=¨#B94A48¨»,«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»q«/mi»«mn»4«/mn»«/msup»«/math»

Therefore, the GCF of «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#B94A48¨»20«/mn»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»p«/mi»«mn»2«/mn»«/msup»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»q«/mi»«mn»2«/mn»«/msup»«/math» and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#B94A48¨»45«/mn»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»p«/mi»«mn»3«/mn»«/msup»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»q«/mi»«mn»4«/mn»«/msup»«/math» is «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#B94A48¨»5«/mn»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»p«/mi»«mn»2«/mn»«/msup»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»q«/mi»«mn»2«/mn»«/msup»«/math».