Prime & Composite Numbers - Varsity Tutors

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Prime & Composite Numbers

Study Guide

Key Definition

A whole number is a prime number with exactly two integral divisors: $1$ and itself. A composite number has more than two divisors.

Important Notes

  • The number $1$ is neither prime nor composite.
  • The number $2$ is the only even prime number.
  • Any number greater than $2$ that is even is not prime.
  • Numbers ending in $0$ or $5$ (except $5$ itself) are not prime.
  • Composite numbers have more than two factors.

Mathematical Notation

$+$ represents addition$-$ represents subtraction$\times$ or $*$ represents multiplication$\div$ or $/$ represents divisionRemember to use proper notation when solving problems

Why It Works

Prime numbers are fundamental in number theory due to their role as building blocks for all numbers. Composite numbers are products of these primes.

Remember

To check if a number is prime, test for divisibility by all prime numbers up to its square root.

Quick Reference

Prime Example:$5$ is primeComposite Example:$4$ is composite

Understanding Prime & Composite Numbers

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

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Beginner Explanation

A prime number has exactly two divisors: $1$ and itself.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

Which of the following is a prime number?

A$11$B$12$C$14$D$15$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

Find out if $37$ is a prime number when splitting snacks.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Determine if $29$ is a prime number.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Which number is composite?

A$31$B$33$C$37$D$41$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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