Mastering Number Properties: Factors, Multiples, Powers & Roots
Mastering Number Properties
Lesson duration is: 180 minItems in this lesson
Mastering Number Properties
What do you already know about factors, multiples, powers, and roots?
Learning Objective
At the end of the lesson you will be able to understand and solve problems involving factors, multiples, powers, and roots.
Key Vocab Overview
Today we will learn about: Factors, Multiples, Prime numbers, Composite numbers, Powers, Exponents, Roots, and Square roots.
What Are Factors?
A factor is a whole number that divides exactly into another number, leaving no remainder.
Factor Examples
For example, 2 and 3 are factors of 6 because 2 × 3 = 6.
What Are Multiples?
A multiple of a number is the product of that number and any whole number.
Multiple Examples
The first five multiples of 3 are: 3, 6, 9, 12, 15.
Retrieval: Check Your Knowledge
Can you list all factors of 12? Can you give three multiples of 5?
Prime and Composite Numbers
Prime numbers have exactly two factors (1 and itself). Composite numbers have more than two factors.
Powers and Exponents
A power shows how many times to multiply a number by itself. Exponent is the name of the small above number.
Worked Example: Powers
2^3 means 2 × 2 × 2 = 8. The base is 2 and the exponent is 3.
What Are Roots?
A root is a number that, when multiplied by itself a specific number of times, gives the original number. For example, the square root of 9 is 3.
Square Roots Symbols
The symbol √ means square root. So, √16 = 4 because 4 × 4 = 16.
Comparing Powers and Roots
Powers are repeated multiplication, roots are the opposite—finding what was multiplied.
Key Terms at a Glance
Factors & Multiples
Factors: Divides exactly, e.g. factors of 8: 1, 2, 4, 8. Multiples: Products, e.g. multiples of 4: 4, 8, 12, 16.
Powers & Roots
Powers: 5^2 = 25. Roots: √25 = 5.
Recap Quiz
1. What is a factor? 2. What is √49? 3. What is 5 × 3 written as a power?
Pause & Reflect
What was the most challenging idea for you in today’s lesson? Write your answer in one sentence.
Write down 3 things you learned in this lesson.
Write down 2 things you want to know more about.
Ask 1 question about something you haven't quite understood yet.
