What is a Factor?
A factor of a number is a whole number that can be multiplied with another whole number to get that number.
In simple words:
A factor is a number that divides another number exactly, without leaving any remainder.
Example:
Factors of 12 are numbers that divide 12 equally.
1 × 12 = 12
2 × 6 = 12
3 × 4 = 12
So, factors of 12 are: 1, 2, 3, 4, 6, and 12.
Notice: Every number has 1 and itself as factors.
Rules of Factors
Let’s make it easy with some golden rules!
Factors are always whole numbers (no decimals or fractions).
Example: 2 is a factor of 10, but 2.5 is not.
1 is a factor of every number.
Example: 1 × 25 = 25 → So, 1 is always included.
The number itself is always a factor.
Example: 25 × 1 = 25 → So, 25 is a factor of 25.
Factors come in pairs.
Example: For 12 → pairs are (1,12), (2,6), (3,4).
How to Find Factors?
There are two main ways kids can find factors:
By Division
Check if a number divides another number without a remainder.
Example: Find factors of 15.
15 ÷ 1 = 15 ✔️
15 ÷ 2 = 7.5 (Not a factor ❌)
15 ÷ 3 = 5 ✔️
15 ÷ 4 = 3.75 (Not a factor ❌)
15 ÷ 5 = 3 ✔️
15 ÷ 15 = 1 ✔️
So, factors of 15 are 1, 3, 5, 15.
By Multiplication
Think of numbers that multiply to make the given number.
Example: Factors of 20
1 × 20 = 20
2 × 10 = 20
4 × 5 = 20
Factors are 1, 2, 4, 5, 10, 20.
Difference Between Factors and Multiples
Many kids get confused between factors and multiples.
Let’s clear it up!
Factors → Numbers that divide a number exactly.
Multiples → The product we get when we multiply the number.
Example with 6:
Factors of 6 = 1, 2, 3, 6
Multiples of 6 = 6, 12, 18, 24, … (goes on forever)
Factors are limited, but multiples are unlimited!
Prime and Composite Numbers with Factors
Prime Numbers
A prime number has only two factors: 1 and itself.
Example:
7 → Factors are 1 and 7.
11 → Factors are 1 and 11.
Composite Numbers
A composite number has more than two factors.
Example:
12 → Factors are 1, 2, 3, 4, 6, 12.
18 → Factors are 1, 2, 3, 6, 9, 18.
Special Types of Factors
Even Factors
Factors of a number that are even.
Example: Factors of 18 → 1, 2, 3, 6, 9, 18
Even factors: 2, 6, 18
Odd Factors
Factors of a number that are odd.
Example: Factors of 18 → Odd factors: 1, 3, 9
Common Factors
Factors that are the same for two or more numbers.
Example:
Factors of 12 → 1, 2, 3, 4, 6, 12
Factors of 18 → 1, 2, 3, 6, 9, 18
Common factors = 1, 2, 3, 6
Factorization
Factorization means breaking a number into its factors.
Example:
24 → 1 × 24
2 × 12
3 × 8
4 × 6
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Another way is Prime Factorization (breaking into only prime numbers).
Example:
24 = 2 × 2 × 2 × 3 = 2³ × 3
Real-Life Examples of Factors
Sharing equally → If you have 20 candies and want to share equally among friends, factors tell you how many friends you can share with.
(2, 4, 5, 10, 20).
Arranging things → Chairs in rows, cupcakes on trays, etc.
Games → Dividing players into equal teams.
Building → Bricks or tiles arranged in rows and columns.
Fun Practice Examples
Find the factors of 16.
1 × 16
2 × 8
4 × 4
Factors = 1, 2, 4, 8, 16
Find the common factors of 30 and 45.
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Factors of 45 = 1, 3, 5, 9, 15, 45
Common = 1, 3, 5, 15
Which number has only 2 factors?
Answer: Prime numbers (like 13 → factors are 1, 13).
Tips to Remember
Factors are always smaller than or equal to the number.
Every number has at least two factors: 1 and itself.
Multiples go on forever, but factors are limited.
Prime numbers = 2 factors, Composite numbers = more than 2 factors.
Summary
A factor is a number that divides another number exactly.
Factors come in pairs and are always whole numbers.
1 and the number itself are always factors.
Prime numbers have only 2 factors, composite numbers have more.
Factors are useful in sharing, arranging, and solving real-world problems.
