Factors And Multiples

Factors & Multiples Explorer | Grade 5 Math

Factors & Multiples 🧩

Master the building blocks of mathematics

👤 Student Explorer

📖 Understanding the Basics

🔍 Factors

Numbers that divide another number exactly (leaving no remainder).

Example: Factors of 6 are 1, 2, 3, and 6.

🚀 Multiples

The result of multiplying a number by 1, 2, 3, and so on.

Example: Multiples of 5 are 5, 10, 15, 20...

👑 The Big Two: HCF & LCM

HCF (Highest Common Factor): The biggest factor shared by two numbers.

LCM (Lowest Common Multiple): The smallest multiple shared by two numbers.

✨ Divisibility Magic Tricks

🔢 Divisible by 2: If it ends in an even number (0, 2, 4, 6, 8).
🔢 Divisible by 5: If it ends in 0 or 5.
🔢 Divisible by 10: If it ends in 0.
🔢 Divisible by 3: If the sum of its digits is divisible by 3.

💡 Step-by-Step Examples

Example 1: List all factors of 12
Step 1
Find pairs that multiply to 12. Let's test them in order:
1 × 12 = 12
2 × 6 = 12
3 × 4 = 12
Final
The Factors of 12 are: 1, 2, 3, 4, 6, 12.
Example 2: Find the HCF of 8 and 12
Step 1
List the Factors of 8: {1, 2, 4, 8}
Step 2
List the Factors of 12: {1, 2, 3, 4, 6, 12}
Step 3
Find the Common Factors: {1, 2, 4}
Final
The highest one is 4. So, HCF = 4!
Example 3: Find the LCM of 3 and 4
Step 1
List Multiples of 3: 3, 6, 9, 12, 15...
Step 2
List Multiples of 4: 4, 8, 12, 16...
Final
The smallest number in both lists is 12. So, LCM = 12!
Example 4: Word Problem 🔔

"Two bells ring every 4 and 6 minutes. When will they ring together next?"

Identify
We need to find the Lowest Common Multiple (LCM) because we want the next shared time.
Step 1
4 min table: 4, 8, 12, 16...
Step 2
6 min table: 6, 12, 18...
Answer
They will ring together at 12 minutes! 🔔🔔

✏️ Quick Practice

1. Is 45 divisible by 5? (Type 'Yes' or 'No')

2. What is the smallest multiple of 7?

3. Find HCF of 5 and 10.

4. Find LCM of 2 and 5.

5. Is 123 divisible by 3? (Hint: 1+2+3=?)

📝 The Ultimate Number Quiz

Q1: Which of these is a factor of 15?

Q2: What is the 5th multiple of 6?

Q3: Is 234 divisible by 2?

Q4: What is the HCF of 9 and 12?

Q5: What is the LCM of 4 and 5?

Q6: Why is 345 divisible by 3?

Q7: How many factors does the number 10 have?

Q8: Which number is a multiple of BOTH 2 and 3?

Q9: Finding common ground: What is the LCM of 10 and 15?

Q10: A florist has 14 roses and 21 lilies. What is the max identical bouquets she can make?

Quiz Complete!

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