How To Find The Greatest Common Factor Quickly!

in this lesson we're going to talk about how to find the greatest common factor so let's say if we have two numbers 15 and 35 what is the greatest common factor between these two numbers here's one method that you can use first write the prime factorization of each number the prime factorization of 15 is simply 3 * 5 you want to break down 15 into prime numbers that multiply to 15 35 is a composite number and it could be broken down into 7 * 5 now once you have the prime factorization of each number notice the common prime numbers that are present so five goes into 15 and 35 so five is a factor of 15 and 35 it's a common factor because it's found in both numbers and it's the greatest of all the common factors factors so it's called the GCF the greatest common factor so the GCF of 15 and 35 is 5 now let's try another example for the sake of practice what is the greatest common factor of 21 and 28 so let's write out the factors of 21 21 is 3 * 7 so that's the prime factorization of 21 28 is 4 * 7 and four can be broken down into to 2 * 2 so this is the prime factorization of 28 notice that 7 is a common factor between 21 and 28 in fact it's the greatest common factor so that's the GCF between 21 and 28 the answer is seven now let's work on another example 22 and 55 go ahead and pause the video find the GCF the greatest common factor between these two numbers 22 is 2 * 11 55 is 5 * 11 the GCF is 11 find the GCF between 12 and 16 so take a minute pause the video and work on that example so 12 is 4 * 3 and four is a composite number which we can break down into 2 * 2 so that's the prime factorization of 12 and for 16 which is 4 * 4 four can be broken up into 2 * 2 and the other four is 2 * 2 as well so it takes four TW to get to 16 now that we've written the prime factorization of 12 and 16 we can identify the greatest common factor so the first number have two twos the last one also have two twos so the greatest common factor is 2 * 2 which is 4 those numbers are common to 12 and 16 do the same thing for 15 and 18 write the prime factorization and then identify the GCF so 15 is simply 3 * 5 we can't break it down any further than that 18 is 6 * 3 and 6 is 3 * 2 and then still have the other three so three is the only common factor in 18 and 15 it's the greatest common factor and so that's the GCF the answer is three now what about 24 and 40 find the GCF between of two numbers so 24 is 4 * 6 and 4 is 2 * 2 6 is 3 * 2 so that's the prime factorization of 2 4 40 is 8 * 5 and 8 is basically 2 * 2 * 2 so 24 has 3 twos and 40 has three twos as well so you want to identify the prime numbers that are the same in both lists so 24 and 40 both contain 3 twos 2 * 2 * 2 that's 8 so 8 is the GCF in this problem and you could check it 40 if you divide 40 by 8 you get five 24 divid 8 you get three so the GCF is going to be divisible 24 and 40 has to be divisible both by the GCF 8 sometimes you may need to find the GCF between two monomials so sometimes variables will be involved what is the greatest common fact fact between 6X and 9 x^2 well the process is the same we need to write the prime factorization of 6X 6 is 3 * 2 and then we have an x 9 x^2 we can break down 9 into 3 * 3 and x^2 is x * X so both lists contains at least one three and an X so therefore the GCF between 6X and 9 x^2 is 3 * X X which is just 3x now what about this one 12x Y and 15 x^2 y Cub find the GCF between these two monomials so let's start with 12xy 12 is 3 * 4 and four we can write it as 2 * 2 and then we have 1 x and one y 15 x^2 y Cub 15 is 3 * 5 and x^2 is x * X Y Cub is y * y * y so let's identify what's common in both lists we have a three there's at least one X and a single Y and that's all that we can find that's common to the two list that we have so the GCF the greatest common factor is 3x y try this one 24 x^2 y cub and 30 x Cub y 4 24 is 4 * 6 and 4 is 2 * 2 6 is 2 * 3 then we have x^2 which is x * X and Y cub which is y * y * y 30 is 5 * 6 and 6 is 2 * 3 let's not forget the five so 30 is 2 * 3 * 5 x Cub is x * x * X Y to 4th is y * y * y four times so two is common to both lists and we have a three as well and then there is is uh two x variables that can be found in both and three y variables so the GCF is going to contain a two a three 2X varibles and three y variables so 2 * 3 is 6 x * X is x^2 3 y's represent y Cub so this is the greatest common factor between these two monomials now what about finding the GCF between three numbers let's say 12 18 and 20 now the process is the same it's simply longer the prime factorization of 12 is 2 * 2 * 3 and 18 that's 3 * 6 and 6 is 3 * 2 let me write it in ascending order so the prime factorization of 18 is 2 * 3 * 3 and for 20 is 4 * 5 and 4 is 2 * 2 now once you have the prime factorization of all three numbers identify what's common to it so each number contains at least one two and not every number has a three or five but all numbers do contain at least one two so therefore two is the GCF between 12 18 and 20 now what about between 30 48 and 56 what is the greatest common factor between those three numbers so 30 is 5 * 6 or 6 * 5 and 6 is 2 * 3 so that's the prime factorization of 30 the prime factorization of 48 is it's 2 * 24 and 24 is 2 * 12 and 12 is 2 * 6 and 6 is 2 * 3 so that's the prime factorization of 48 and 56 is 2 * 28 28 is 2 * 14 14 is 2 * 7 now let's find out what's common to everything all three numbers contain at least one two not all of them contain a three 56 doesn't have a three involve and not all of them contain a five or a seven so once again the GCF is simply two

Channel: The Organic Chemistry Tutor

Views: 435,945

Keywords: finding the greatest common factor of monomials, finding the greatest common factor of large numbers, finding the greatest common factor, monomials, large numbers, two numbers, three numbers, greatest common factor, gcf, with exponents, with variables

Id: BIlF65I2EwA

Length: 10min 28sec (628 seconds)

Published: Mon Jul 17 2017