How to Find the GCF using Prime Factorization | 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 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 3 times 3 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 seven 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 2 2 3 and 7 2 times 2 times 3 times 7 equals 84. now we need to find any common prime factors three is a common prime factor and 7 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 7 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 2 times 6 equals 12 so 2 and 6 are factors 2 is prime so we are done there but we can break 6 down further 2 times 3 equals 6 so 2 and 3 are factors 2 is prime so we are done there and 3 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 2 times 9 equals 18 so 2 and 9 are factors 2 is prime so we are done there but we can break nine down further three times three equals nine so 3 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 using prime factorization I hope that helped thanks so much for watching until next time peace foreign