Download PA_M3_S1_T3_GCF Transcript

PA_M3_S1_T3_GCF Transcript
So let's look at finding the greatest common factors, or greatest common
divisors, and the greatest common factor, or the greatest common divisor,
is simply the largest number that will evenly divide two or more numbers.
So let's look at these first numbers, 105 and 42, I am going to write the
factors of 105 over here so 1*105, 2 doesn't go into 105 because it's not
even, 3 goes into 105, times 35, 5 goes into 105, 21 times, and 7 goes in
15 times.
On 42 I have 1*42, 2*21, and now that I have this much I can see that I
already have my greatest common factor of 21 in both cases because it
appears very quickly in the 42 and each of them is paired by a prime
number, so in this case 2 and 5. That tells me that that's going to be
my greatest common factor so the GCF of 105 and 42 is 21.
Let's look at the next one. 36 and 120, I'm going to do the same thing.
I'm going to write some factors down, 1*36, 2*18, 3*12, 4*9, 5 doesn't go
in, but we do get 6*6. On 120 we have 1* 120, 2*60 3*40, 4*30, 5*24,
6*20, 8*15, and 10*12. Once they have only factors written out, then I
can go back and see what number is greatest between these pairs. As I go
through them I've got 1, 2, 3, 4, 6; 1, 2, 3, 4, 6 - and I don't have
any 8 on 36 and I don't have any 10 on 36, but I do have 12. When I go
through all of those, I find that 12 is my greatest common factor, or
greatest common divisor, for 36 and 120.
Let's look at a case where I have three numbers and I want to find the
greatest common factors. I'll do the same thing again, 1*24, 2*12, 3*8,
and 4*6. Those are my factors of 24.
For 30 I have 1*30, 2*15, 3*10, 4 doesn't go in, but I do get 6*5. And
then for 36 I have 1*36, 2*13, 3*12, 4*9 and 6*6. When I look at this,
this is all the factors I could possibly have, but you'll notice that I
had a common factor of 6 in each of them so that my greatest common
factor for 24, 30, and 36 is equal to 6 and these are the largest numbers
in each case that will evenly divide the numbers I've been given.
This is how you go about finding your greatest common factor.