Theory of Positive Integers

An exploration of the properties, relationships, and applications of positive integers in various mathematical contexts.

Introduction to Positive IntegersDivisibility and MultiplesPrime Numbers and Composite Numbers
Greatest Common Divisor and Least Common MultipleThe Fundamental Theorem of ArithmeticNumber Patterns and Sequences
Using Positive Integers in Everyday LifePositive Integers in TechnologyOrganizing Events and Schedules
Breaking Down Problems with FactorizationUsing Patterns to Predict and Solve
Introduction to Posi...Divisibility and Mul...Prime Numbers and Co...Greatest Common Divi...The Fundamental Theo...Number Patterns and ...Using Positive Integ...Positive Integers in...Organizing Events an...Breaking Down Proble...Using Patterns to Pr...
Basic Concepts

Divisibility and Multiples

Understanding Divisibility

Divisibility means one number can be divided by another without a remainder. For example, 12 is divisible by 3 because \( 12 \div 3 = 4 \), with nothing left over!

What Are Multiples?

A multiple of a number is what you get when you multiply that number by a positive integer. For example, multiples of 5 are 5, 10, 15, 20, etc.

Useful Tricks

  • A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8.
  • A number is divisible by 5 if it ends in 0 or 5.

Where Do We See This?

Divisibility and multiples help us with time (minutes in an hour), organizing teams, and finding even groups.

Examples

  • 24 is divisible by 6 because \( 24 \div 6 = 4 \).

  • Multiples of 7: 7, 14, 21, 28.

In a Nutshell

Divisibility and multiples show how numbers fit together and help in grouping and sharing.

Next
Prime Numbers and Composite Numbers