How to Find the GCF (2 Different Ways) | Greatest Common Factor | Math with Mr. J

welcome to math with Mr J [Music] in this video I'm going to cover how to find the greatest common factor also known as the GCF using two different strategies listing out factors and prime factorization we're going to start by looking at the strategy of listing out all of the factors of the numbers in order to find the greatest common factor then we'll move to using prime factorization now as far as the greatest common factor between numbers this is going to be the largest factor in value that both numbers share factors are the numbers that can be multiplied to equal a given number or you can think of factors as the numbers a given number can be divided by evenly so divided with no remainder now it's not the most technical or mathematical way to word it but you can think of factors as the numbers that go into the given number so again the greatest common factor is going to be the greatest or largest factor in value that both numbers share that both numbers have in common let's jump into our examples and see exactly what this looks like starting with number one where we have 16 and 24. we first need to list the factors of each number let's start with the factors of 16. now I would suggest always starting with the factors of 1 and the number itself because we know one times that number will equal that number itself we can think of factors in terms of pairs 1 times 16 equals 16 or we can think of it in terms of division we can divide 16 by those factors evenly however you want to think about it so I'm going to write 1 and 16 with a gap in between for the other factors that way we can write the factors in order now we need to list the other factors of 16. so let's think about what else goes into 16 so to speak think about multiplication facts division facts and we can work our way up from one so there are different strategies and ways to work through this the next factors of 16 are 2 and eight two times eight equals sixteen so two and eight are factors of 16. and then our last factor of 16 is four four times four equals sixteen so four is a factor of 16. although four times four equals sixteen we only need to write four Once in our factors list and that's it for the factors of 16. you can always think about other possible factors if you're unsure if you're done for example three five six and so on but we have them all the factors of 16 are one two four eight and sixteen let's move on to the factors of 24. we will start with 1 and 24. next we have two and twelve two times twelve equals twenty four so two and twelve are factors of 24. then we have three foreign and eight three times eight equals twenty four so three and eight are factors of 24 and then lastly we have four and six four times six equals twenty four so four and six are factors of 24. and that's it for the factors of twenty four one two three four six eight twelve and twenty four now that we have the factors listed for our numbers we need to look for common factors and specifically the greatest common factor so let's look for factors that these numbers share that they have in common so one is a common factor two is a common factor four is a common factor and then eight is a common factor so the greatest common factor is eight the greatest factor in value that they share the greatest factor in value that they have in common so the GCF the greatest common factor is eight the greatest common factor of 16 and 24 is 8. let's move on to number two where we have 15 and 35. let's start with the factors of 15. we have one and fifteen next we have three and five three times five equals fifteen so three and five are factors of 15. and that's it for the factors of fifteen one three five and fifteen now let's list the factors of 35 so we have one and thirty-five and then five and seven five times seven equals thirty-five so five and seven are factors of 35 and that's it for the factors of 35 1 5 7 and 35. now that we have our factors list for our numbers we need to look for common factors and specifically the greatest common factor so one is a common factor and then 5 is a common factor that means 5 is the greatest common factor so the GCF the greatest common factor is five the greatest common factor of 15 and 35 is 5. so there's how we list factors in order to find the greatest common factor let's move on to using prime factorization here are our examples for using prime factorization now I like using this strategy and find it helpful when working with numbers that are a little larger in value and not as simple to work with for example the strategy of listing out all of the factors of the numbers in order to find the GCF can be kind of difficult and time consuming when working with larger numbers in value so this is a different approach a different strategy to be familiar with when it comes to finding the greatest common factor let's jump into our examples starting with number one where we have 63 and 84. let's start with the prime factorization of 63 and we will start with the factors of 7 and nine seven times nine equals 63 so 7 and 9 are factors of 63. now 7 is prime so we are done there 9 we can break down three times three equals nine so three is a factor of nine three is prime so we are done there and there and that's the prime factorization of 63. we can't break that down any further now we have the prime factorization of 84. let's start with the factors of 2 and 42 2 times 42 equals 84. so 2 and 42 are factors of 84. now 2 is prime so we are done there 42 we can break down 2 times 21 equals 42. so 2 and 21 are factors of 42. 2 is prime so we are done there 21 we can break down three times 7 equals 21. so 3 and 7 are factors of 21. three is prime and 7 is prime as well so we are done that's the prime factorization of 84. we can't break that down any further now that we have the prime factorization of both of those numbers we need to find common prime factors so prime factors that they share now I'm going to list the prime factors of each to make it easier to find the ones they have in common so as far as 63 we have three three and seven three times three times seven equals 63. 484 we have two two three and seven two times two times three times seven equals 84. now we need to find any common prime factors three is a common prime factor and seven is a common prime factor so they have a 3 and a 7 in common once we find those common prime factors we multiply them so three times seven and that equals 21 and that's our greatest common factor so the GCF the greatest common factor of 63 and 84 is 21. let's move on to number two where we have 48 and 72. let's start with the prime factorization of 48 and we will start with the factors of 2 and 24. 2 times 24 equals 48 so they are factors now 2 is prime so we are done there we can break down 24. 2 times 12 equals 24 so 2 and 12 are factors 2 is prime so we are done there we can break 12 down further two times six equals 12. so 2 and 6 are factors 2 is prime so we are done there but we can break 6 down further two times three equals six so two and three are factors 2 is prime so we are done there and three is prime so we are done there as well and we are done with the prime factorization of 48. we can't break that down any further now we need the prime factorization of 72. let's start with the factors of 2 and 36 2 times 36 equals 72 so they are factors 2 is prime so we are done here 36 we can break down 2 times 18 equals 36 so 2 and 18 are factors 2 is prime so we are done there 18 we can break down two times nine equals eighteen so two and nine are factors 2 is prime so we are done there but we can break nine down further three times three equals nine so three is a factor of nine three is prime so we are done there and there and we are done with the prime factorization of 72. we can't break that down any further now that we have the prime factorization of both 48 and 72. we need to find common prime factors so I'm going to write the prime factors of 48 and 72 that way it's a little easier to find common prime factors for 48 we have two two and three so two times two times two times two times three equals 48 472 we have two two two three and three two times two times two times three times three equals 72. now we need to find common prime factors they have a 2 in common another two in common another two in common and then a three in common so now that we found the common prime factors we need to multiply them to get the greatest common factor so we have two times two times two they have three twos in common times three two times two is four times two is eight times three is 24. so the GCF the greatest common factor of 48 and 72 is 24. so there you have it there's how to find the greatest common factor the GCF using two different strategies listing out factors and using prime factorization I hope that helped thanks so much for watching until next time peace