Factors
Any whole number greater than one can be factored, which means it can be broken down into smaller integers.
Learning Objective

Calculate numbers' factors and prime factors
Key Points
 Factorization (or factoring) is the process of breaking an object (such as a number or algebraic expression) down into a product of other objects, or factors, which when multiplied together give the original number or expression.
 Prime factorization is a particular type of factorization that breaks a number of interest into prime numbers that when multiplied back together produce the original number.
 Every positive integer greater than 1 has a distinct prime factorization.
 Factor trees can be used to find the prime factorization of a number.
Terms

prime factor
A factor that is also a prime number.

factor
Any of various objects multiplied together to form some whole.

factorization
The process of creating a list of items that, when multiplied together, will produce a desired quantity or expression.

prime number
A whole number greater than 1 that can be divided evenly by only the number 1 and itself.
Full Text
In mathematics, factorization (or factoring) is the process of breaking an object (such as a number or algebraic expression) down into a product of other objects, or factors, which when multiplied together give the original number or expression. The aim of factoring is to reduce something to "basic building blocks." This process has many reallife applications and can help us solve problems in mathematics.
In particular, factoring a number means to break it down into numbers that when multiplied back together produce the given number. For now, we will focus on factoring whole numbers.
For example, consider the number 24. To find the factors, consider the numbers that yield a product of 24. We know that
Prime Factorization
Prime factorization is a particular type of factorization that breaks a number of interest into prime numbers that when multiplied back together produce the original number. Such prime numbers are called prime factors.
Example 1
For example, consider the number 6. We know that
Example 2
Now, consider the number 12. We know that
Factor Trees and Prime Factorization
Every positive integer greater than 1 has a distinct prime factorization. To factor larger numbers, it can be helpful to draw a factor tree.
In a factor tree, the number of interest is written at the top. Then, two factors of that number are found and connected below that number with branches. This process repeats for each subsequent factor of the original number until all the factors at the bottoms of the branches are prime.
Prime factorization example
This factor tree shows the factorization of 864. It shows that 864 is the product of five 2s and three 3s. A shorthand way of writing these resulting prime factors is
Key Term Reference
 Interest
 Appears in these related concepts: Interest Compounded Continuously, Accounting for Interest Earned and Principal at Maturity, and Tax Considerations
 expression
 Appears in these related concepts: Compound Inequalities, Sets of Numbers, and Simplifying, Multiplying, and Dividing
 factoring
 Appears in these related concepts: Factoring Accounts Receivable, Rational Algebraic Expressions, and Selling to Consumers
 focus
 Appears in these related concepts: Parabolas As Conic Sections, What Are Conic Sections?, and Types of Conic Sections
 integer
 Appears in these related concepts: Scientific Notation, Binomial Expansions and Pascal's Triangle, and Finding a Specific Term
 product
 Appears in these related concepts: Measuring Reaction Rates, Writing Chemical Equations, and Basic Operations
Sources
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