Factor using GCF

welcome to mumo Math and Science in this video let's talk about factoring using the GCF and um let's just remember this uh there's a couple steps and so basically remember g d l you're going to find the greatest common factor then you're going to divide and then you're going to lead with the greatest common factor so let's get started with this example and I'm going to move this up and so here we first thing we need to do is find the greatest common factor of 4 A7 - 16 a 4th okay so I like to use a factor tree in order to find the greatest common factor so uh let's get started okay the speed things along I went ahead and completed a factor tree and I wrote the um prime numbers in this box and the rule is is since we have two numbers if there's two in a column you bring it down and then you multiply we do not bring the three down CU there's not two in that column and then if you multiply this 4 8 it's 16 now many of you could have just said okay I know the common uh greatest common factor of the coefficients is 16 but I wanted to show how you can find that now but we aren't finished okay so let's write 16 and then what we do is we find for com we look for common variables we have a and a that's common and then we take the smallest exponent and that is four so now we have the greatest common factor of these two now what we do is we divide okay so I'm going to so it's not confusing looking 48 a 7th / 16 a 4 minus 16 a 4th / 16 a to 4th now when we we divide let's go ahead and do this 16 goes into um 483 * uh bring down the A and that will be 7 - 4 so that's a 3r minus 16 / 16 is 1 and then these cancel okay so now we need to go back so we've gotten the G the greatest common factor we have divided now we need to leave with the co with the greatest common factor and that is 16 a to 4th so there it is factored I'll Circle okay so the factored 48 a 7th - 16 a 4th factor is this okay let's work another example okay remember we're going to use g d L greatest common factor divide lead with the greatest common factor so now we need to find the greatest common factor of these two monomials okay so uh let's get started I know many of you can probably glance and see that the greatest common factor is nine but I'm going to create a factor tree just so you know how I found that okay so here's the factor tree of 9 3 and three and a 54 prime numbers I'll Circle them and then what I've done is I've written them in this box and remember the rule is that if you have to have two in a column to bring the number down so we have three and three so that equals nine now uh we need to go over here and we need to um find the variables so we have nine and so we have an X and an X and the lowest um expon onent is one and then we have a y and a y and the lowest exponent is three so here is the greatest common factor so we have this portion done now let's divide we have 9 x^2 y 4 / 9 x y 3r + 54x y cubed over 9 x y I CU so when we divide 9 / 9 is 1 uh X um bring down the x 2 - 1 is 1 and then with the Y 4 - 3 is 1 plus 9 goes into 54 6 times uh the X's cancel the Y's cancel okay so let's put this in parenthesis remember you don't have to have the one in front of it now remember we can't forget we've got to lead we've got this done we've got to lead with our um greatest common factor so that is 9x y Cub so here is it factored this binomial factored becomes this thanks for watching and remember kindness multiplies kindness be kind to someone today