Prime and composite numbers
🎯 In this topic you will
- Find prime numbers up to 100
- Understand the difference between prime and composite numbers
🧠 Key Words
- composite number
- factor
- multiple
- prime number
Show Definitions
- composite number: A number that has more than two factors, meaning it can be divided evenly by 1, itself, and at least one other whole number.
- factor: A whole number that divides exactly into another number with no remainder.
- multiple: A number produced by multiplying a given number by a whole number (e.g., 12 is a multiple of 3).
- prime number: A number greater than 1 that has exactly two factors: 1 and itself.
Remembering Factors
You already know how to find factors of numbers.
Numbers with Two Factors
Some special numbers have exactly two factors. For example, the number 3 has factors 1 and 3, and the number 7 has factors 1 and 7.
💡 Quick Math Tip
Two-factor rule: If a number has exactly two factors — 1 and itself — then it is a prime number.
What We Call These Numbers
These special numbers are called prime numbers.
A Fun Challenge
Can you think of any other prime numbers?
Why Prime Numbers Matter
Prime numbers are very important! Adults often buy goods online using a credit card. Every time they send a credit card number over the internet, it is converted into a code which is based on prime numbers!
❓ EXERCISES 3.3
1. Which of these numbers are prime numbers?
$11 \quad 21 \quad 31 \quad 41 \quad 51 \quad 61$
How do you know they are prime numbers?
👀 Show answer
They are only divisible by $1$ and themselves.
2. Which number could be the odd one out?
$19 \quad 39 \quad 49$
Give two different answers and explain your reason.
👀 Show answer
• $19$ is the only prime number.
• $39$ is the only multiple of $3$.
• $49$ is the only square number ($7^2$).
Any two valid reasons accepted.
3. Copy and complete this sentence.
A number with more than two factors is called a _____ number.
👀 Show answer
4. Copy this Venn diagram and write each number in the correct place.
$15 \quad 16 \quad 17 \quad 18 \quad 19$
👀 Show answer
$18$ → even only
$17$ and $19$ → prime only
$15$ → outside all sets (not square, not prime, not even)
5. Arun and Zara play a game of ‘What’s my number?’
| Arun says: | Zara replies: |
|---|---|
| Is the number less than $20$? | No |
| Is the number less than $25$? | Yes |
| Is the number even? | No |
| Is the number prime? | Yes |
What is the number?
👀 Show answer
6. Here are four digit cards.
$\boxed{1} \quad \boxed{2} \quad \boxed{5} \quad \boxed{9}$
a. A prime number
b. A multiple of $3$
c. A square number
d. A factor of $36$
Discuss your answers with your partner.
👀 Show answer
a. $19$ or $29$
b. $12$, $15$, or $21$
c. $25$
d. $12$
🧠 Think like a Mathematician
Here are some digit cards: 2, 3, 5, 6, 7, 8, 9
Use all the cards to make four prime numbers.
Each digit must be used exactly once.
Challenge
How many different solutions can you find?
Follow-up Questions
👀 show answer
- 1. One valid solution is the four primes: $23$, $59$, $7$, $89$ (using all digits from 2,3,5,6,7,8,9).
- 2.
- $23$ is divisible only by 1 and 23.
- $59$ is divisible only by 1 and 59.
- $7$ is a known prime number.
- $89$ is divisible only by 1 and 89.
- 3. Yes. There are multiple possible solutions because the digits can be rearranged into different combinations that still produce four prime numbers, provided that each digit is used exactly once.