Pro Mode Academy
Pro ModeAcademy
Login
MATHEMATICSNumber & Arithmetic
CURRENT TOPICFactors & Multiples
×
÷
● Master Guide Core Concepts

Factors, Multiples & Prime Factors

Understand how numbers fit together. Master factor rainbows, times tables multiples, prime factor branching, and Venn diagrams for HCF & LCM.

Practice Levels:Warm-UpCore ModePro Mode

Your Learning Mission

Master these skills to become a Maths Champion!

Finding Factors

List all whole numbers that divide another number exactly without remainders.

Finding Multiples

List product numbers in times tables going on forever.

Prime Numbers

Understand numbers with exactly two unique factors (1 and itself).

Common Factors/Multiples

Calculate Highest Common Factors (HCF) and Lowest Common Multiples (LCM).

🟩

Factors: The Dividing Buddies

Definition: Whole numbers that fit exactly inside another number without leaving any remainders!

💡 Example: Factors of 24 are numbers that divide 24 cleanly → 1, 2, 3, 4, 6, 8, 12, and 24.
🤝 Always in Pairs: Factors love buddies! E.g. for 24: 1×24, 2×12, 3×8, 4×6.
🎯 Start & End: Every number has 1 and itself as factors. The largest factor is always the number itself!
🔍 Exam Use: We list factors to find the **Highest Common Factor (HCF)** of two numbers.
Factor Rainbow Explorer
1234681224

Factor Pairs

1 × 24 = 242 × 12 = 243 × 8 = 244 × 6 = 24
🟪

Multiples: The Times Table Rockets

Definition: The numbers you get when you multiply a number by other whole numbers (its times table!).

💡 Example: First 6 multiples of 6 are just its times table → 6, 12, 18, 24, 30, and 36.
🚀 Goes On Forever: Multiples are infinite. Unlike factors, they never stop growing!
🌱 Starting Point: Every number is a multiple of itself. The smallest multiple is the number itself!
⚡ Exam Use: We list multiples to find the **Lowest Common Multiple (LCM)** of two numbers.
Multiples Pattern & LCM Grid
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Common Multiples (1-100): 24, 48, 72, 96...
🌟 Lowest Common Multiple (LCM) is 24

Factors vs Multiples Showdown

🎮 Interactive Showdown Checker
Choose a number:
Factors of 12

1, 2, 3, 4, 6, 12

(6 numbers divide A)
Multiples of 12

12, 24, 36, 48...

(Infinite times table)
➗Team FactorsNumbers that divide IN exactly
✖Team MultiplesNumbers we multiply OUT to make tables
Finite & Limited
Size
Infinite & Endless
1 and the number
Include
Starts at the number
Smaller or equal
Value
Larger or equal
HCF (Highest Factor)
Exams
LCM (Lowest Multiple)
🌟

Special Numbers Rules

🟢

Prime Numbers (The Unsplittables): Numbers that have exactly two factors: 1 and itself (e.g. 2, 3, 5, 7, 11...).

🟡

Composite Numbers (The Builders): Numbers that have more than two factors (e.g. 4, 6, 8, 9, 12...).

🔴

Number 1 (The Lone Ranger): It has only one factor (itself), which makes it neither prime nor composite!

🔍

How to Find Prime Factors

Divide step-by-step by prime numbers (2, 3, 5, 7...) until you reach 1.

  1. Start with the smallest prime number (usually 2). Does it divide exactly? Divide it!
  2. Keep dividing the result by the smallest prime possible.
  3. Stop when you reach 1. The primes you used are your prime factors!
💡 Example: 24 = 2 × 2 × 2 × 3. The prime factors of 24 are 2 and 3.
🌳 Interactive Tool

🌲 Grow Your Own Prime Factor Tree!

Pick a number below to split it down into its unsplittable prime factors. Watch how the branches grow!

24
2
12
2
6
2
3

Prime Factorization Ingredients

24 = 2 × 2 × 2 × 3

🟢 Circled green nodes are **Prime Numbers** (unsplittable!). 🟣 Purple nodes are **Composite Numbers** (can be split!).

Distinct Prime Factors: 2 and 3

🧠

HCF & LCM Made Simple (Venn Diagram Method)

Learn how prime factors unlock the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of two numbers.

🎯 Highest Common Factor (HCF)The largest factor that divides both numbers exactly. Example: HCF of 12 and 18 is 6.
🚀 Lowest Common Multiple (LCM)The smallest number in both times tables. Example: LCM of 12 and 18 is 36.
🤝 Interactive Walkthrough

Venn Diagram Explorer (HCF & LCM)

See how Venn Diagrams make finding HCF and LCM super easy and fun!

🔮 Step 1: Pick Two Numbers!
Number A:
Number B:
🤖

Concept: The Story of Prime Houses

Let's split 12 and 18 into prime factors. Primes unique to 12 live in the left circle, unique to 18 live in the right circle. Primes that are best friends and live in BOTH move to the Shared Middle Room!

House 12
House 18
2
3
2
3
Prime factors of 12:2 × 2 × 3
Prime factors of 18:2 × 3 × 3

Cheat Codes & Quick Tips

➗

Use Division

Divide step-by-step to list factors cleanly in pairs.

✖

Times Tables

Use times tables to verify and count multiples quickly.

🔢

Sort In Order

Always list factors and multiples in order to avoid missing pairs.

💪

Practice Daily

Memorise primes up to 20 to speed up calculations.

🧩 Try These Challenge Questions

Submit your answers to test your 11+ vocabulary mastery.

Score: 0 / 5
1. List the factors of 36 (comma separated).
2. List the first 6 multiples of 9 (comma separated).
3. Find the HCF of 36 and 45.
4. Find the LCM of 15 and 20.
5. Find the prime factors of 84 (comma separated).
Golden Mnemonic Rule
🟩 Factors go in⇄🟪 Multiples go out

🚀 Ready to Practice?

Test your skill with our graded assessments