Factors and Multiples Infographic

WHAT ARE THEY?

★ FACTORS: Numbers that divide a number exactly with no remainder.
★ MULTIPLES: Numbers obtained by multiplying a number by whole numbers (1, 2, 3 ...).
★ They help us in everyday life in counting, grouping, sharing, arranging and solving problems.

Let's explore factors and multiples! 🔍

FACTORS

MULTIPLES

If a number divides another number exactly, it is a factor of that number.

Example: Factors of 12

1, 2, 3, 4, 6, 12

Check:

12 ÷ 1 = 12

12 ÷ 2 = 6

12 ÷ 3 = 4

12 ÷ 4 = 3

12 ÷ 6 = 2

12 ÷ 12 = 1

Multiples are the numbers we get by multiplying a number by whole numbers.

Example: Multiples of 4

4 × 1 = 4 | 4 × 2 = 8

4 × 3 = 12 | 4 × 4 = 16

4 × 5 = 20 | 4 × 6 = 24

4 × 7 = 28 | 4 × 8 = 32

4 × 9 = 36 ...

Multiples of 4 are:
4, 8, 12, 16, 20, 24, 28, 32, 36 ...

QUICK FACTS 💡

★ Every number has at least two factors – 1 and the number itself.
★ 1 is a factor of every number.
★ Every number has infinite multiples.
★ All even numbers have 2 as a factor.
★ All odd numbers have 1 as a factor.
★ A number is a multiple of itself.

6 12 18

1. FACTORS

Factors are numbers that divide a number completely.

Example 1: Factors of 18

Find pairs of numbers whose product is 18:

1 × 18 | 2 × 9 | 3 × 6

So, factors of 18 are: 1, 2, 3, 6, 9, 18

Example 2: Factors of 36

Pairs: 1×36 | 2×18 | 3×12 | 4×9 | 6×6

So, factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

💡 Observation: Factors always come in pairs.
Small factor × Big factor = Number

2. MULTIPLES

Multiples are found by multiplying the number by 1, 2, 3, 4 ...

Example 1: First 10 multiples of 6

6 × 1 = 6 | 6 × 2 = 12

6 × 3 = 18 | 6 × 4 = 24

6 × 5 = 30 | 6 × 6 = 36

6 × 7 = 42 | 6 × 8 = 48

6 × 9 = 54 | 6 × 10 = 60

So, multiples of 6 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60 ...

Example 2: First 8 multiples of 9

9, 18, 27, 36, 45, 54, 63, 72 ...

💡 Observation: Multiples keep going on forever.

∞

3. HOW TO FIND FACTORS?

Step 1: Start from 1 up to the number.

Step 2: Check which numbers divide the number exactly (remainder = 0).

Step 3: List them in order.

Example: Find factors of 24

Num	24 ÷ Num	Rem	Num	24 ÷ Num	Rem
1	24÷1 = 24	0 ✓	7	24÷7 = 3 rem 3	X
2	24÷2 = 12	0 ✓	8	24÷8 = 3	0 ✓
3	24÷3 = 8	0 ✓	9	24÷9 = 2 rem 6	X
4	24÷4 = 6	0 ✓	10	24÷10 = 2 rem 4	X
5	24÷5 = 4 rem 4	X	11	24÷11 = 2 rem 2	X
6	24÷6 = 4	0 ✓	12	24÷12 = 2	0 ✓

So, factors of 24 are:
1, 2, 3, 4, 6, 8, 12, 24

✏️ 7. PRACTICE TIME!

A. FIND THE FACTORS

1) Factors of 15: ________

2) Factors of 28: ________

3) Factors of 32: ________

4) Factors of 45: ________

5) Factors of 50: ________

B. FIRST 10 MULTIPLES

1) Multiples of 7: ________

2) Multiples of 9: ________

3) Multiples of 11: ________

4) Multiples of 3: ________

5) Multiples of 8: ________

C. COMMON FACTORS & GCF

1) Factors of 16 & 24:

Common factors:______

GCF =______

2) Factors of 20 & 30:

Common factors:______

GCF =______

D. COMMON MULTIPLES & LCM

1) Multiples of 5 & 10:

Common multiples:______

LCM =______

2) Multiples of 6 & 9:

Common multiples:______

LCM =______

8. REAL LIFE EXAMPLES

🍎

Sharing 24 apples equally among 6 friends.
(Factors help in equal grouping/sharing)

🚌

Buses come every 15 mins, trains every 20 mins. When do they meet together?
(LCM helps find concurrent intervals)

📐

Tiles of size 12 cm and 18 cm are laid in a hall. What is the largest square tile used exactly?
(GCF helps find largest shared dimensions)

9. CHALLENGE YOUR MIND!

1) Find the LCM of 6, 8 and 12. _____

2) Find the GCF of 36, 48 and 60. _____

3) Word Problem: A bell rings every 8 minutes and another bell rings every 12 minutes. If both rang together at 9:00 a.m., when will they ring together again?

Ans: _________

🏆 Be smart, be fast, be accurate!

10. TIPS TO REMEMBER

✓ List factors in pairs.
✓ Check divisibility carefully.
✓ Multiples go on forever.
✓ Practice daily to become a master!