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# Prime factorization exercise

## Video transcript

we're asked what is the prime factorization of 36 let me get my little scratch paper out so the prime factorization of 36 so let's start with the smallest prime number we know and that is 2 and think about this to go into 36 well sure it does 36 is 2 times 18 so we can write that down 36 is 2 times 18 so now we have 36 as a product of a prime number and 18 is clearly a composite number it has factors other than 1 and 18 so let's try to factor this further so is this divisible by 2 sure 18 is 2 times 9 2 times 9 so now 9 is a composite number that we haven't fully factored obviously the twos are both prime 9 is not divisible by 2 but it is divisible by 3 9 is 3 times 3 so we can say that 36 36 is equal to 2 times 2 times 3 times 3 this is its prime factorization all of these numbers are prime so now let's input that let's input that into to make sure we got it right 2 times 2 times 3 times 3 and you can check yourself if you have the product of numbers that are all prime and the product actually is 36 you have successfully prime factorize the number let's do a couple more of these what is the prime factorization of 30 I'll get my scratch paper out again so we'll do the same process so 30 well it's divisible by 2 so we can write that as 2 times 15 15 isn't divisible by 2 but it is divisible by 3 it's the same thing as 3 times 5 and both 3 and 5 are prime numbers they're only divisible by 1 and themselves so the prime factorization of 30 is 2 times 3 times 5 let's enter that in so it is 2 times 3 times five let's do one more of these what is the prime factorization of 73 now 73 is interesting it looks whoops 73 I'll get my scratch paper out for this we could try to factor 73 so you might try to well this is clearly an odd number so - is it going to be divisible into 73 you might try three you would immediately see well three is divisible into 72 if you divide into 73 you have a remainder of 1 4 isn't it divisible well 4 isn't a prime number so we wouldn't even try 5 is it divisible into 73 doesn't end in a 5 or 0 7 is not divisible into 73 7 goes into 70 so you'd have a remainder of 3 11 isn't divisible into 73 is divisible into 66 or 77 so not 73 so it looks as I test more and more numbers it doesn't look like there's any easy thing that divides into 73 so I'm willing to go with 73 itself is a prime number so this is its prime factorization you that's the it's just 73 so let's write that down so the answer here let's just write 73 and you don't want to write one time 73 because 1 is not a prime number you just want to remember 1 is it's only as one factor itself a prime factor has a prime number has two factors 1 and itself 2 different prime factors 1 and itself in itself is not 1 so we just want to write prime numbers here 73 is a prime number let's check our answer and we got it right