BasicMathSkills AddSubtractDecimals InverseOperations
ComplementarySupplementary MultiplyDecimals NumberProperties
item8 Exponents OrderofOperations-GEMA1
VerticalAngles FactorTrees item3a
AreaofPolygons Fractions ProportionsRatios
AreaofParallelogram AddSubtractFractions Quadrilaterals1
AreaofRectangle multiplyfractions RationalNumbers
AreaofSquare dividefractions SieveofEratosthenes
AreaofTrapezoid lowesttermsfractions
AreaofTriangle mixednumbers
CirclesandPi Integers ClassNews
Circumference AddSubtractIntegers item24
AreaofCircle MultiplyDivideIntegers item17
Prime Factorization & Factor Trees

Let’s learn about prime factorization.

Lesson 1: Vocabulary Review

Let's review some vocabulary.

prime number: any positive integer with EXACTLY two factors is a prime number, 1 and itself

factors: the numbers you multiply together to get the product— algebraically it would look like this

ab = c where a and b are the factors and c is the product

composite number: positive integers that have THREE or more whole number factors

Lesson 2: Using a Factor

What if you want to find all of the factors of a number? How could you do it? EASY! Use Prime Factorization! In fact, get out your Sieve of Eratosthenes to help you. This is a great tool because it can help provide a way for you to check for prime numbers.

Prime Factorization is a method used to find all of the prime factors of a number. It utilizes a tree diagram for organizing your factors.

Let’s try it using the number 24.


Step 1: Make a tree

Start by writing the number and then drawing two tree branches underneath.

Step 2: Begin factoring…

Think of the factors of the number (or, if this seems hard, think, "What can I divide this number evenly by?" since sometimes it is easier to think backwards). Write down the two numbers at the end of the tree branches.
Keep factoring the numbers…until you get down to prime numbers.
In this next example, you will see how the numbers 4 and 6 have been factored further until we get down to the primes.

Step 3: Circle the Prime Numbers

When you get to the prime factors, circle them.

Step 4: Write the Prime Numbers using Exponents

Re-write the prime numbers as an expression, using exponents. Voila!

If you want even MORE practice, then click More Prime Factorization Practice.

©2009–2016 Sherry Skipper Spurgeon.

All Rights Reserved.