Prime or Composite

Learning Objectives Define prime numbers. Define composite numbers. Distinguish between prime and composite numbers. Identify all factors of a given whole number. Determine if a given whole number (up to 100) is prime or composite. Explain why 0 and 1 are neither prime nor composite. Apply divisibility rules to aid in classifying numbers. Ever wonder why some numbers seem 'lonely' with only two friends, while others have a whole party of friends? 🤔 Let's uncover the secret lives of numbers! In this lesson, you'll learn to classify whole numbers greater than 1 as either prime or composite. Understanding these classifications is fundamental to number theory and helps us break down numbers into their basic building blocks, which is super useful in many a...

TermDefinitionExample Whole NumberThe set of non-negative integers: 0, 1, 2, 3, and so on, without fractions or decimals.5, 12, 0, 100 are all 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 (more than two factors). Divisibility RulesShortcuts or tests to determine if a number is divisible by another number without performing long division.A number...

Prime Number Rule A whole number $p > 1$ is prime if its only positive factors are $1$ and $p$. To identify a prime number, you must find exactly two factors: 1 and the number itself. If you find any other factor, it's not prime. Composite Number Rule A whole number $c > 1$ is composite if it has at least one positive factor other than $1$ and $c$. To identify a composite number, you need to find at least one factor other than 1 and the number itself. This means it has more than two factors. Special Cases of 0 and 1 The numbers $0$ and $1$ are neither prime nor composite. Always remember these two exceptions. 1 only has one factor, and 0 has an infinite number of factors, so they don't fit the definitions.