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Factors

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Factors

Study Guide

Key Definition

Factors are numbers that can be multiplied together to get another number. For example, $5 \times 2 = 10$, so 5 and 2 are factors of 10.

Important Notes

Factors of integers must be whole numbers, but polynomial factors can include expressions with non-integer coefficients.
Every non-zero integer has at least two positive factors: 1 and itself. (Note: 0 is divisible by every non-zero integer and does not have a finite set of factors.)
A common factor is a factor that two or more numbers have in common.
$x+1$ can be a factor of a polynomial such as $x^2-2x-3$.
Factorization is the process of breaking down a number into its factors.

Mathematical Notation

$\times$ represents multiplication

$\div$ represents division

Remember to use proper notation when solving problems

Why It Works

Understanding factors helps in simplifying fractions and solving polynomial equations using $factorization$.

Remember

Every nonzero integer is divisible by its factors (positive and negative) without a remainder. Positive integers have a finite set of factors, while polynomials can have infinitely many real factors when scalar multiples are counted.

Quick Reference

Example:$10 = 2 \times 5$

Understanding Factors

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Factors are numbers that multiply to create another number. E.g., $2 \times 5 = 10$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following is a factor of $10$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $10$ candies to share equally among friends. How many friends can you fairly divide the candies among?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

How would you explain the concept of common factors to a friend using the numbers $12$ and $18$?

Challenge Quiz

Single Choice Quiz

Advanced

Which expression can be a factor of the polynomial $x^2-2x-3$?

Recap

Watch & Learn

Review key concepts and takeaways