Einstein on a chalk board.

GCF --Greatest Common Factor

  • Greatest Common Factoring GCF
  • Every number that is not a prime can be factored into its primes.
  • The GCF or greatest common factor is made up of all the primes that are common to all the numbers.
  • Find the GCF of 18, 24, 36 and 48. First factor all the numbers into their primes, then bring down the primes individually that are common to all the numbers.
  • Lastly multiply all the common primes to make up the G.C.F
  • So, the GCF is the result of the primes multiplied together = 6
  • In the case of exponents choose the lowest exponent
  • Now when we combine both variables the rules still apply.
  • Find the GCF (greatest common factor) for
  • Factor all 3 values and pull out their common values.
  • Note: We could have broken 10 into 25. Since 10 was common to all 3 values it was just as easy not to break it down.
  • Note 1: We also used the lowest value of the exponent of x which was 3.
  • What do we know so far about Factoring?
  • Factoring undoes multiplying.
  • If we have 2 factors we can FOIL them to create a trinomial. (Polynomial with 3 terms with descending exponents of x).
  • See explanation on FOIL.
  • We have a method for doing the reverse process which is factoring a trinomial.
  1. Factor the third term (into nm factors)
  2. Add the third term factors together to get the middle term.(which are n+m factors). Note only use the term   which applies to the middle term including the correct sign. The outcome is of the form
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