Finding the Greatest Common Factor

You might be asked to factor an algebraic expression on the GED math test. When you factor something all you need to do is provide the largest possible numbers that were multiplied to get to that algebraic expression. Let’s say you’re given

6n² + 15n

What numbers when multiplied will give you both 6 and 15?

Six can be multiplied by one to get 6, but six can’t be multiplied by anything to get 15, so move on.

How about 3? Yes three can be multiplied by 2 to get 6 and by 5 to get 15.

So provide the threes on both sides as well as what you need to multiply the threes by to get 6 and 15. Break the variables apart from the coefficients as well.

Now take the largest terms that both sides have in common, 3 and n, and put them outside the parentheses.


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  • abby

    Could you please do a few more?

  • rey

    so in this problem what happened to the other 3 would u have to combine the 3s?

    • Devone

      You don’t have to list BOTH 3’s.. It just asks for the LARGEST terms that BOTH sides have in common.. Not how MANY..I hope this can help you to understand it.. It took me a minute to figure it out as well..

  • Dan

    I HATE greatest common factor… this is the one thing in math that I can never get. And yes I know my multiplication tables, but it takes forever to have to sit there and list all of the freaking factors. It’s so frustrating. Wish there was a faster, and more efficient way to find the factors without a calculator.

  • abraham nieves

    need more practice

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