Prime Factorization
A prime factorization of a composite number is a way of expressing the composite number as a product of its prime factors. We can use a tree diagram to find the prime numbers of the composite number we are trying to factorize.
Examples
Tree Diagram and Division Table
Tree Diagram Steps
Step 1: Write 60 on the top of the tree.
Step 2: Choose a pair of factors for 60 as branches.
Step 3: Choose a pair of factors for 6 and 10.
6 = 3 x 2
10 = 5 x 2
Step 4: 2, 2, 3, and 5 are on the last row and are the prime factors.
Division Table Steps
Step 1: Divide 24 by the smallest prime number, the smallest prime number should divide the number exactly, which is 2 in this case
Step 2: Divide the quotient, which is 12, by the smallest prime number
Step 3: Repeat the process until the quotient becomes 1
Step 4: Lastly, once you have all the prime factors, multiply them together.
2 x 2 x 2 x 3 = 24
Why?
It is important to know prime factorization because it can help you find the least common multiple (LCM). Which is an important skill to know in math and will make solving math problems much easier and efficient for you. We also use prime factorization on a daily basis which can be used in money exchange, calculating costs, time estimation, etc. I used a tree diagram as an example because it is an easy way to find prime factors of composite numbers and a great way if you are a visual learner.
Vocabulary
Factors– A number that divides another number
Factor pairs– A set of two whole numbers and when multiplied it results in a specific product
Prime number– A whole number which has exactly two factors, and the two factors are always 1 and the number itself
Composite number– A whole number that has more than two factors
Prime factors– Prime factors of a whole number are the factors of the number which are prime
Division Table photo source:
Admin. “Prime Factorization – Definition, Methods, Examples, Prime Factorize.” BYJUS, BYJU’S, 30 Nov. 2021, https://byjus.com/maths/prime-factorization/.