Prime Factorization (Intro and Factor Trees)

prime factorization of 18
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prime factorization factor trees before we get into prime factorization there are two key ideas to review first that factors are the numbers you multiply together to get another number as the product second a prime number has exactly two factors 1 and itself and since youve worked with prime numbers before you should remember that the first few prime numbers are 2 3 5 7 11 and 13 mathematicians call prime numbers the building blocks of all positive whole numbers because every whole number greater than 1 is either a prime number or a composite number the word composite means made up of various parts each composite number is made up of a single set of prime factors in other words you can get to every composite number by multiplying a single set of prime numbers together we call these the prime factors of a

number Ill show you how this idea stacks up for the numbers up to 15 prime numbers in red and composite numbers in blue 2 is prime 3 is prime for comes from 2 times 2 5 is prime we get 6 from 2 times 3 7 is prime 8 comes from 2 times 2 times 2 9 is from 3 times 3 we get 10 from 2 times 5 11 is prime 12 is from 2 times 2 times 3 13 is prime 14 is from 2 times 7 and we get 15 from 3 times 5 prime factorization means finding that single set of prime numbers that multiply up to a given composite number to do a prime factorization we can use a factor tree to help us split each composite number apart into its prime factors lets do an example 18 we split

18 into factors until we cant split any more I am using red for prime numbers and blue for composite numbers I say to myself 18 comes from 2 times 9 I circled 2 as a prime number I will come back to it later 9 is a composite number so I split it down I get 9 from 3 times 3 3 is a prime number so I circle both of them – I have no composite numbers left so now I know I have found all the prime factors next to the factor tree I restate the prime factors 2 times 3 times 3 is 18 its correct but its not quite finished to do a really great job on prime factorization we show a factor that is repeated by using exponents we call it using exponential notation it sounds fancy but its easy

enough check it out how many 3s have I got – so I say 2 times 3 to the power 2 because 3 is used twice is 18 it makes the final answer very tidy notice that I listed the prime factors from smallest to largest that is the standard way of listing prime factors and you should do that too heres something cool it doesnt matter how you split your composite numbers down you always come out with the same prime factors I could have done it differently and said 18 is from three times six six is from two times three I still get the same prime factors of 2 times 3 times 3 or 2 times 3 to the power 2 different way of getting there but its still the same result one more example and then its your turn we will do

the prime factorization of 48 I know that 4 times 12 is 48 this time I have 2 composite numbers to work on the 4 and the 12 4 comes from 2 times 2 2 is prime so I Circle them both and move on to the 12 12 comes from 2 times 6 and 6 is from 2 times 3 I circle all the primes no more composite numbers are left so Im ready next we collect all the primes we circled 2 times 2 times 2 times 2 times 3 is 48 and for a great final answer we use our exponential notation to tidy up those repeated factors to came up 4 times so we say 2 to the power 4 times 3 is 48 and thats all you need to do now its over to you have fun with prime factorization you

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