Question

2. How did you find the GCF of the variables in each term?

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Answer 1

Answer:

You can also determine the GCF if you have both numbers and variables. Factorize the numbers and identify all common factors. To get the GCF multiply all common factors. You can use the greatest common factor to simplify fractions.

Answer 2

GCF or Greatest common factor is the collection of all the common factors or variables present in the equations.

• Let us explain the procedure to find the GCF by taking the example as follows: 4x⁴y - 6x³yz + 8x²y²
• Begin by finding common factors among the constants in front.  Looking at the example, the constants 4, 6, & 8 have a common factor of 2.
• After finding common constants, look for common variables.
• In the example, x and y occur in all three terms. Once the common variables are identified, find the lowest exponent on each.  
• In the example, the lowest exponent on x is 2 and the lowest exponent on y is 1.  Therefore, x² and y can be factored out (the 1 on y is only written for example, and would not appear in the answer).
• Just as you would divide each term by 2 when factoring out the 2, you need to divide each term by x²y when factoring out the x²y.
• After factoring, the example would appear as 2x²y(2x² - 3xz + 4y).
• This is how we find the GCF of the variables in each term.