Mathematics
Grade 8
15 min
Prime or Composite Numbers
Prime or Composite Numbers
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Introduction & Learning Objectives
Learning Objectives
Identify factors and multiples of a given whole number.
Define and differentiate between prime and composite numbers.
Classify any whole number greater than 1 as either prime or composite.
Apply divisibility rules to efficiently determine factors of a number.
Determine if a number is prime by systematically testing for divisibility by smaller prime numbers.
Explain why the number 1 is neither prime nor composite.
Ever wondered why some numbers seem 'indivisible' while others can be broken down into many parts? 🕵️♀️ Let's uncover the secret lives of numbers!
In this lesson, you'll learn to categorize whole numbers greater than 1 as either prime or composite based on their factors. Understanding these fundamental building blocks of num...
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Key Concepts & Vocabulary
TermDefinitionExample
Whole NumberThe set of non-negative integers {0, 1, 2, 3, ...}. For prime and composite numbers, we focus on numbers greater than 1.5, 12, 0, and 100 are whole numbers.
FactorA whole number that divides another whole number exactly, leaving no remainder.The factors of 12 are 1, 2, 3, 4, 6, and 12 because each divides 12 evenly.
Prime NumberA whole number greater than 1 that has exactly two distinct positive factors: 1 and itself.7 is a prime number because its only factors are 1 and 7.
Composite NumberA whole number greater than 1 that has more than two distinct positive factors.10 is a composite number because its factors are 1, 2, 5, and 10.
DivisibilityThe ability of one number to be divided by another number without a remainder.20 is divisible by 5 because 20 ÷ 5...
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Core Formulas
Definition of a Prime Number
A whole number $p > 1$ is prime if its only positive factors are 1 and $p$.
To check if a number is prime, find all its factors. If there are only two (1 and the number itself), it's prime.
Definition of a Composite Number
A whole number $c > 1$ is composite if it has more than two positive factors.
To check if a number is composite, find all its factors. If there are more than two, it's composite.
The Number 1
The number 1 is neither prime nor composite.
This is a special case. Prime numbers must have *exactly* two factors, and composite numbers must have *more than two* factors. The number 1 has only one factor (itself).
Divisibility Test for Primes
To determine if a number $N$ is prime, you only need to test for d...
5 more steps in this tutorial
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Challenging
To verify that 211 is a prime number, what is the complete list of prime numbers you must test for divisibility?
A.2, 3, 5, 7
B.2, 3, 5, 7, 9, 11
C.2, 3, 5, 7, 11, 13
D.All prime numbers up to 105
Challenging
A student incorrectly claims that 111 is a prime number. Which statement best explains their error?
A.The student is correct; 111 is a prime number.
B.The student forgot the divisibility rule for 3; since 1+1+1=3, 111 is divisible by 3.
C.The student forgot to check for divisibility by 7.
D.The student assumed it was prime because it is an odd number.
Challenging
The numbers 2 and 3 are consecutive whole numbers that are both prime. Why can there be no other pair of consecutive whole numbers that are both prime?
A.In any pair of consecutive whole numbers greater than 2, one of them must be an even number, and therefore composite.
B.All prime numbers greater than 3 are odd, so they cannot be consecutive.
C.The gap between prime numbers increases as the numbers get larger.
D.One of the numbers in any consecutive pair must be divisible by 3.
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