“Learning Factors and Multiples with Easy Tricks and Activities”(2025)

 

“Learning Factors and Multiples with Easy Tricks and Activities”(2025)

Introduction

 

Understanding factors and multiples is a fundamental skill in mathematics that helps in solving problems related to division, fractions, and number patterns. Whether you're preparing for exams or just strengthening your math skills, mastering these concepts with simple tricks can make learning fun and easy.

In this blog, we’ll cover:
 Definitions of factors, multiples, prime & composite numbers
 Easy tricks to find HCF & LCM
 Odd & Even numbers explained
 Prime factorization made simple
 Story sums & activities for better understanding

Let’s dive in!

 

1. Basic Definitions

Factors

A factor of a number is an integer that divides it exactly without leaving a remainder.
Example:

• Factors of 12: 1, 2, 3, 4, 6, 12 (because 12 ÷ 1 = 12, 12 ÷ 2 = 6, etc.)

Multiples

A multiple of a number is the product of multiplying two numbers.
Example:

• Multiples of 5: 5, 10, 15, 20, 25,… (because 5×1=5, 5×2=10, etc.)

Prime Numbers

A prime number has only two factors—1 and itself.
Examples: 2, 3, 5, 7, 11, 13,…

Composite Numbers

A composite number has more than two factors.
Examples: 4, 6, 8, 9, 10,…

Odd & Even Numbers

• Even numbers are divisible by 2 (e.g., 2, 4, 6, 8,…).
• Odd numbers are not divisible by 2 (e.g., 1, 3, 5, 7,…).

2. HCF & LCM Made Super Easy! (With Tricks!)

Finding HCF (Highest Common Factor) and LCM (Least Common Multiple) doesn’t have to be hard! Here are more tricks to make it faster and easier.

 

Trick 1: Factor Pairs

• To find factors, pair numbers that multiply to give the original number.
  Example (Factors of 18):
  1 × 18 = 18
  2 × 9 = 18
  3 × 6 = 18
  Factors: 1, 2, 3, 6, 9, 18

Trick 2: Divisibility Rules

• A number is divisible by:
• 2 if it ends in 0, 2, 4, 6, or 8.
• 3 if the sum of its digits is divisible by 3.
• 5 if it ends in 0 or 5.

 

1. HCF Tricks (Beyond Listing Factors)

Trick 1: Prime Factorization Method (Best for Large Numbers)

1.   Break both numbers into prime factors.

2.   Multiply the common prime factors with the lowest power.
Example: Find HCF of 36 & 60

• Prime factors of 36 = 2 × 2 × 3 × 3 = 2² × 3²
• Prime factors of 60 = 2 × 2 × 3 × 5 = 2² × 3¹ × 5¹
• Common primes: 2² & 3¹
• Highest Common Factor = 2 × 2 × 3 = 12

Faster than listing all factors!

Trick 2: Division Method (Euclid’s Algorithm)

1.   Divide the larger number by the smaller number.

2.   Replace the larger number with the remainder.

3.   Repeat until remainder = 0. The last divisor is the HCF.
Example: HCF of 56 & 32

• 56 ÷ 32 = 1 (Remainder = 24)
• Now, 32 ÷ 24 = 1 (Remainder = 8)
• Now, 24 ÷ 8 = 3 (Remainder = 0)
• HCF = 8

  Best for very large numbers!

 

2. LCM Tricks (Beyond Listing Multiples)

Trick 1: Prime Factorization Method

1.   Break both numbers into prime factors.

2.   Take the highest power of each prime and multiply.
Example: LCM of 12 & 18

• Prime factors of 12 = 2² × 3¹
• Prime factors of 18 = 2¹ × 3²
• Highest powers: 2² × 3²
• LCM = 4 × 9 = 36

  Works every time!

Trick 2: HCF & LCM Relationship

• HCF(a,b) × LCM(a,b) = a × b
• So, LCM = (a × b) ÷ HCF
  Example: Find LCM of 15 & 20
• First, find HCF of 15 & 20 → 5
• Now, LCM = (15 × 20) ÷ 5 = 300 ÷ 5 = 60

 Saves time if you already know HCF!

Trick 3: The "Ladder Method" (For Multiple Numbers)

1.   Write numbers side by side.

2.   Divide by common primes until no common factors remain.

3.   Multiply all divisors and remaining numbers.
Example: LCM of 12, 18, 24

 

2 | 12, 18, 24 

2 | 6, 9, 12 

3 | 3, 9, 6 

3 | 1, 3, 2 

2 | 1, 1, 2 

   | 1, 1, 1 

 

LCM = 2 × 2 × 3 × 3 × 2 = 72

Great for 3+ numbers!

 

3. Bonus Shortcuts

For HCF:

• If two numbers are consecutive (e.g., 14 & 15), their HCF is 1 (they are co-prime).
• If out of two numbers one number is a multiple of the other, the smaller number is the HCF.
• Example: HCF of 8 & 24 → 8

For LCM:

• The LCM of two co-prime numbers (HCF=1) is their product.
• Example: LCM of 5 & 7 → 35
• If one number is a multiple of the other, the larger number is the LCM.
• Example: LCM of 6 & 18 → 18

 

4. Practice Problems

Q1. Find HCF of 48 & 72 (Use prime factorization).
Q2. Find LCM of 9 & 12 (Use the HCF-LCM relationship).
Q3. Three bells ring every 6, 8, and 12 seconds. When will they ring together? (Use the ladder method).

Answers:

• A1: HCF = 24
• A2: LCM = 36
• A3: After 24 seconds

 

Final Tip:

• For HCF, think "smallest common division."
• For LCM, think "next shared multiple."
• Always check divisibility rules to save time!

3. HCF & LCM Made Easy

HCF (Highest Common Factor)

• It is the largest number that divides two or more numbers completely without leaving any remainder.
  Trick: List all factors and pick the greatest common one.
  Example: HCF of 12 & 18
• Factors of 12 are: 1, 2, 3, 4, 6, 12
• Factors of 18 are: 1, 2, 3, 6, 9, 18
  Common factors: 1, 2, 3, 6 → HCF = 6

LCM (Least Common Multiple)

• Least common multiple is the smallest number that is a multiple of two or more numbers.
  Trick: List multiples and pick the smallest common one.
  Example: LCM of 4 & 6
• Multiples of 4: 4, 8, 12, 16,…
• Multiples of 6: 6, 12, 18, 24,…
  Common multiple: 12 → LCM = 12

 

4. Prime Factorization (Easy Method)

Breaking down a number into its prime factors.

Trick: Division Method

Example: Factorize 24

1.   Divide by the smallest prime (2): 24 ÷ 2 = 12

2.   Divide again by 2: 12 ÷ 2 = 6

3.   Divide by 2 : 6 ÷ 2 = 3

4.   Now, 3 is a prime number.
Prime factors of 24: 2 × 2 × 2 × 3 (or 2³ × 3)

Prime Factorization Explained in Detail (With Easy Tricks!)

Prime factorization is like taking a number apart to find its building blocks - the prime numbers that multiply together to make it. Let me break this down step by step with clear explanations and extra tips!

 

What is Prime Factorization?

It's expressing a number as:

• A product of only prime numbers
• Each prime is called a "prime factor"
• Every number has a unique prime factorization

Detailed Step-by-Step Example: Factorizing 24

Step 1: Always Start with the smallest prime number (2)

• Question: Is 24 divisible by 2?
   Yes! (All even numbers are divisible by 2)
• Calculation: 24 ÷ 2 = 12
  → First factor found: 2

Step 2: Factorize the result (12)

• Question: Is 12 divisible by 2?
   Yes!
• Calculation: 12 ÷ 2 = 6
  → Second factor: 2
  (Now we have: 2 × 2)

Step 3: Continue with the next result (6)

• Question: Is 6 divisible by 2?
   Yes!
• Calculation: 6 ÷ 2 = 3
  → Third factor: 2
  (Now: 2 × 2 × 2)

Step 4: Final number (3) is prime

• Check: 3 is only divisible by 1 and itself → prime!
• → Final factor: 3
  (Complete factorization: 2 × 2 × 2 × 3)

Final Answer:

24 = 3 × 2 × 2 × 2
(or in exponential form: 2³ × 3¹)

 

Pro Tips for Faster Prime Factorization

1. Division Shortcuts

• Divisible by 2? → Number ends in 0,2,4,6,8
  Example: 48 → ends with 8 → divisible by 2
• Divisible by 3? → Sum of digits is divisible by 3
  Example: 123 → 1+2+3=6 → 6 is divisible by 3 → 123 is divisible by 3
• Divisible by 5? → Ends with 0 or 5

1.   Factor Tree Method 

 

       24

      /  \

     2    12

         /  \

        2    6

            /  \

           2    3

 

• Start with 24, split into 2 × 12
• Split 12 into 2 × 6
• Split 6 into 2 × 3
• All branches end with primes!

3. Handling Odd Numbers

For numbers not divisible by 2, start testing with 3, 5, 7... in order.

Example: Factorizing 45

• 45 ÷ 3 = 15 → factor 3
• 15 ÷ 3 = 5 → another 3
• 5 is prime → stop
• Result: 3 × 3 × 5 (or 3² × 5)

 

Common Mistakes to Avoid

1.   Forgetting to check divisibility by smaller primes first
(Always start with 2, then 3, then 5...)

2.   Stopping too early

o   Incorrect: "50 = 2 × 25" → 25 can still be factored (5 × 5)!

o   Correct: "50 = 2 × 5 × 5"

3.   Missing repeated factors

o   For 8, write 2 × 2 × 2 (not just "2")

 

Practice Problems (With Answers)

1.   Factorize 36
→ Answer: 2 × 2 × 3 × 3 (or 2² × 3²)

2.   Factorize 100
→ Answer: 2 × 2 × 5 × 5 (or 2² × 5²)

3.   Factorize 81
→ Answer: 3 × 3 × 3 × 3 (or 3⁴)

 

Why Prime Factorization Matters

• Simplifies fractions (reducing to lowest terms)
• Helps find HCF and LCM quickly
• Used in cryptography and computer science!

Try it yourself with your favorite numbers! 

5. Practical Story Sums

Problem 1 (HCF Application)

Riya has 15 chocolates and 20 candies. She wants to pack them into boxes with equal numbers of chocolates and candies. What’s the greatest number of boxes she can make?
Solution: Find HCF of 15 & 20 → 5 boxes

Problem 2 (LCM Application)

Two traffic lights blink every 6 and 8 seconds. After how many second will they blink together?
Solution: Find LCM of 6 & 8 → 24 seconds.

Problem 3 (HCF Application - Classroom Supplies)

Story:
A teacher has 12 pencils and 36 erasers. She wants to distribute them equally among students so that each student gets the same number of pencils and the same number of erasers. What is the maximum number of students she can distribute them to?

Solution:

• Find the HCF of 12 (pencils) and 36 (erasers).
• Factors of 12: 1, 2, 3, 4, 6, ,12
• Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
• HCF = 12

Answer: The teacher can distribute supplies to a maximum of 12 students (each gets 1 pencil and 3 erasers).

 

Problem 4 (LCM Application - Bus Schedules)

Story:
Bus A arrives at a station every 15 minutes, and Bus B arrives every 20 minutes. If both buses arrive together at 8:00 AM, at what time will they next arrive together?

Solution:

• Find the LCM of 15 and 20 to determine the next common arrival time.
• Prime factorization:
• 15 = 3 × 5
• 20 = 2² × 5
• LCM = 2² × 3 × 5 = 60 minutes (1 hour)

Answer: The buses will next arrive together at 9:00 AM.

 

Why These Problems Matter

• HCF (Greatest Common Divisor): Solves problems about splitting items into equal groups (e.g., distributing supplies, arranging objects).
• LCM (Least Common Multiple): Solves problems about recurring events (e.g., schedules, timetables, synchronized actions).

Try These Extensions!

1.   HCF Challenge: A gardener has 18 roses and 27 sunflowers. How many identical bouquets can she make using all flowers? (Answer: HCF=9 → 9 bouquets)

2.   LCM Challenge: Two alarm clocks beep every 10 minutes and 12 minutes. If they beep together at noon, when’s the next simultaneous beep? (Answer: LCM=60 → 1:00 PM)

 

 

 

Fun Math Activities:

Learning math doesn’t have to be boring! Here are engaging, hands-on activities to help students (or even adults!) understand factors, multiples, prime numbers, HCF, and LCM effortlessly.

 

1. Factor Hunt

Objective: Quickly list all factors of a given number.

How to Play:

• Teacher/Parent calls out a number (e.g., 24).
• Students/Children race to write all its factors (1, 2, 3, 4, 6, 8, 12, 24).
• First to finish correctly wins!

Bonus Twist:

• Use a timer (e.g., 30 seconds).
• Team version: Groups compete to list factors on a board.

2. Prime or Composite?

Objective: Identify if a number is prime or composite.

How to Play:         

• Call out numbers randomly (7, 12, 19, 21, 29).
• Students/Children stand up for prime, sit for composite.
• Eliminate those who make mistakes—last standing wins!

Memory Trick:

• Prime numbers = "Unbreakable" (only 1 & itself).
• Composite = "Breakable" (can split into smaller factors).

 

3. LCM Bingo (Group Game)

Objective: Find the LCM of two numbers quickly.

How to Play:

1.   Prepare Bingo Cards with numbers like 12, 18, 24, 30, 36, etc.

2.   Call out pairs (e.g., "4 & 6" → LCM = 12).

3.   Students / children mark the LCM if they have it.

4.   First to complete a row shouts "BINGO!"

 Pro Tip:

• Use small numbers first (e.g., 3 & 5 → 15) before harder ones (e.g., 8 & 12 → 24).

 

4. More Easy & Fun Activities!

Activity 4: Factor Dice Roll

Materials: Two dice, paper, pen.
How to Play:

1.   Roll two dice (e.g., 4 & 5 → 20).

2.   List all factors of the product (20: 1, 2, 4, 5, 10, 20).

3.   Most factors in 3 rounds wins!

Why it works: Helps with quick multiplication + factor recognition.

Activity 5: Prime Number Jump

Materials: Number cards (1-50) placed on the floor.
How to Play:

• Call out "Prime" or "Composite".
• Students jump on the correct numbers.
• Eliminate those who step on the wrong type.

Bonus: Add "1" (neither prime nor composite) for a trick question!

Activity 6: Human Factor Tree

Objective: Break down numbers into prime factors physically.
How to Play:

1.   Assign students as numbers (e.g., 24, 12, 6, 3, 2).

2.   They link arms to form a factor tree (24 → 2 × 12 → 2 × 6 → 2 × 3).

3.   Last group standing correctly factorized wins!

Great for kinesthetic learners!

Activity 7: HCF & LCM Word Problem Race

How to Play:

1.   Write real-life problems on cards (e.g., "Two buses come every 10 & 15 minutes—when will they meet?").

2.   Teams solve and grab the correct LCM/HCF answer from a pool.

3.   Fastest team with most correct answers wins!

Example Problem:

• "A baker packs 27 cupcakes and 36 cookies into identical boxes. What are the maximum boxes?" (Answer: HCF=9)

 

Why These Activities Work

 Visual & Hands-On: Helps memory retention.
Competitive Fun: Encourages quick thinking. Real-World Links: Shows why math matters (e.g., schedules, packing items).

Conclusion : Learning factors, multiples, prime numbers, HCF, and LCM doesn’t have to feel like a chore—it can be an exciting adventure! By using real-world examples, fun games, and simple tricks, we’ve seen how these concepts apply to everyday life, from packing gifts to scheduling buses.

Math isn’t about memorizing—it’s about understanding patterns and solving puzzles. Whether you’re a student, teacher, or just brushing up, keep practicing with curiosity and creativity.

Stay curious, keep calculating, and remember—every math problem has a solution waiting for you to discover!