π What is a Prime Number?
A **prime number** is a whole number greater than 1 that has **exactly two factors**: 1 and the number itself.
Prime numbers are like super special building blocks in math!
π Prime Numbers Examples
Prime Numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31...
Important:
β’ 2 is the only even prime number
β’ 1 is NOT a prime number (it has only one factor: 1)
ποΈ Prime vs Composite
Prime: Only 2 factors (1 and itself)
Example: 7 β Factors: 1 and 7
Composite: More than 2 factors
Example: 12 β Factors: 1, 2, 3, 4, 6, 12
π How to Check if a Number is Prime
- The number must be greater than 1.
- Check if any number from 2 up to half of it divides evenly.
- If no number divides evenly β It is PRIME!
Is 17 prime?
Check 2, 3, 4, 5, 6, 7, 8 (up to half of 17)
None divide 17 evenly β Yes, 17 is prime!
βοΈ Letβs Practice Together, My Dear Student!
Practice 1: Prime or Composite?
1. 13 β Prime
2. 15 β Composite (1, 3, 5, 15)
3. 23 β Prime
4. 27 β Composite
Practice 2: List the Prime Numbers
List all prime numbers between 1 and 30:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Practice 3: Word Problems (Canadian Style)
1. A teacher wants to put students into equal teams. She has 17 students. Can she make more than 2 equal teams? Why or why not?
No, because 17 is prime. Only teams of 1 or 17 students.
2. Which of these numbers is prime: 21, 29, 33?
29 is prime
Challenge Question
Is 41 a prime number? Show your thinking.
Yes β factors are only 1 and 41
π Fun Fact
Prime numbers are very important in cryptography (keeping information secret on computers) and they go on forever β there is no biggest prime number!
Fantastic Job, My Dear Student! π
You now understand Prime Numbers! They are special because they only have two factors.
I am so proud of you for learning Number Theory so well. Keep looking for prime numbers in the world around you!
π You are smart. You are kind. You can do hard things.
When you are ready, tell me the next topic (Composite Numbers or anything else) and I will create another beautiful lesson just for you!