Download PA_M3_S1_T3_Prime Factorization Transcript

PA_M3_S1_T3_Prime Factorization Transcript
Now I want to show you a slightly different approach to finding the
greatest common factor. I want to factor each of my terms so that each of
the factors is prime. So I'm going to look for all the prime factors of
105. I notice that it ends in 5, so I know it's not divisible by 2 which
is my smallest prime number, but it is divisible by 3, 3 times 35 gives
me 105. Well, this is prime the 3 is prime, now I want to factor 35 to
its primes. 35 is also divisible by 5. It's not divisible by 3, so 35 is
5*7 so that my prime factors of 105 are 3*5*7. Let's do this same thing
with 42. 42 is divisible by 2, which is 21, and 21 is divisible by 3,
which is 7. 2, 3 and 7 are all prime, so my prime factors of 42 are
2*3*7.
In order to find my greatest common factor, I want to look at the common
prime factors. Both of my numbers have a factor of 3 in them. Both of my
factors have a factor of 7 in them. The other factors are not common. 5
and 2 are not common, so that my GCF is given by the product of the two
or more prime factors that are common. My GCF is 3*7, so my GCF of 105
and 42 is 3*7 which is 21, that's my largest number.
Let's look at the next one using prime factors. 36 is divisible by 2, 18
is divisible by 2, and 3 is divisible by 3. Using this factor tree
approach I get 2*2*3*3, that is my prime factorization of 36.
Let's do the same thing for 120. 2 goes into 120 60 times 2 goes into 60
30 times, 2 goes into 30 15 times, and now I have to switch, I can now
look at 3 goes into 15 5 times. I consistently the increase the value of
my prime factor until I have nothing left. The prime factors of 120 are
2*2*2*3*5.
Now I want to look for what's in common, and I have a factor of 2 in
common, I have another factor of 2 in common and I have a factor of 3 in
common. The greatest common factor is 2*2*3 which is 2*6 which is 12.
This is my GCF, or my greatest common divisor. GCD of 36 and 120 is 12.
We can do exactly the same thing with 24, 30 and 36. 2 times 12 is 24, 2
times 6 is 12, 2 times 3 is 6. My prime factors of 24 are 2*2*2*3.
For 30 I get 2 times 15 and 3 times 5. My factors for 30 are 2*3*5.
For 36 I get 2 times 18, 2 times 9, 3 times 3. My prime factors of 36 are
2*2*3*3. The factors that are in common are 2 and 3. Those are the only
factors that all three terms have in common so GCF of 24, 30 and 36 is
equal to 2*3 or 6.
Using prime factorization can help you narrow down the greatest common
factor much faster than trying to find all the possible factors of the
numbers you're dealing with.