Factors
2026-02-28 08:53 Diff
https://brightchamps.com/en-us/math/numbers/factors

722 Learners

Last updated on November 11, 2025

Every number has factors, but have you ever wondered why some numbers have only two factors while others have many? The number of factors depends on the properties of the number itself. Factors play a crucial role in mathematics, they help us simplify problems and discover other properties, such as the LCM, HCF, and multiples.

Importance of Factors in Math

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

Factors are very helpful in solving all kinds of math problems. A few points that explain the importance of factors in math are:

  • Factors can play a significant role in simplifying issues, as they can help reduce fractions to their simplest form. 
  • LCM and HCF can be calculated using factors.

In real-life scenarios, too, factors can be used to create groupings, divisions, and so on. 
 

What are Factors?

A factor is a number that divides another number exactly, leaving no remainder. Factors and multiples play an essential role in everyday life, from arranging objects in equal groups and managing money to identifying number patterns, solving ratios, and simplifying or expanding fractions.

Properties of Factors

  • Every number has a finite number of factors, where it has a fixed count of factors.
     
  • A factor of a number is always less than or equal to the number itself.
     
  • Every number, except 0 and 1, has at least two factors 1 and the number itself.
     
  • Division and multiplication are the main operations used to find factors of a number.
     
  • All factors are whole numbers, as factors cannot be fractions or decimals.

Explore Our Programs

How to Find Factors?

To find the factors of a number, we can use two main approaches the division method and the multiplication method. Let’s explore how each of these methods works in the sections below.

How to Find Factors Using Division Method

Step 1:
To find the factors of 18 using the division method, start dividing 18 by numbers beginning from 1 and continue up to 18. We list all the numbers that divide 18 exactly (without leaving a remainder).

Step 2:
The numbers that divide 18 are entirely called its factors. We record each number along with its pair and list them as shown. For example:
18 ÷ 1 = 18 is (1, 18)
18 ÷ 2 = 9 is (2, 9)
18 ÷ 3 = 6 is (3, 6)
18 ÷ 4 remainder (not a factor), and so on.
Here, the divisor and the quotient are both factors of the number. So, (1, 18), (2, 9), and (3, 6) are the factor pairs of 18.

Step 3:
After listing all pairs, we can write the complete set of factors of 18 in order, starting from 1 and ending at 18.
Hence, the factors of 18 are 1, 2, 3, 6, 9, and 18.

Finding Factors Using Multiplication Method

Now, let’s find the factors of a number using the multiplication method.
This process is very similar to the division method the only difference is that here we identify two numbers that multiply together to give the given number.
For example:
1 × 18 = 18
2 × 9 = 18
3 × 6 = 18
Hence, the factors of 18 are again 1, 2, 3, 6, 9, and 18.

Finding Factors using the Rainbow Method

Step 1: We know 1 and 60 are factors, and 2 and 30 are also factors of 60.
There are no whole numbers between 1 and 2 that divide 60, so there are no other factors between 30 and 60.

Step 2: Next, we look at 3 and 20. Since there are no whole numbers between 2 and 3, there are no other factors between 20 and 30.

Step 3: Then, we find 4 and 15. There are no numbers between 3 and 4 that divide 60, so no new factors appear between 15 and 20.

Step 4: Now, check 5 and 12 both divide 60 thoroughly.
Again, no numbers between 4 and 5 divide 60, so no new pairs are found between 12 and 15.

Step 5: Finally, look at 6 and 10. There are no whole numbers between 5 and 6 that divide 60 evenly.

Step 6: We test the numbers between 6 and 10, 7, 8, 9 , and see that none of them divide 60 exactly.

Different Types of Factors

Factors play an important role in algebra and arithmetic. Here are some of the key topics we learned about factors.

Prime Factors

Prime factors are prime numbers. Therefore, these factors can only be divisible by 1 and the original number itself. Prime factorization is a process of breaking down a given number into its prime factors. It is like breaking down a LEGO creation into its basic parts. Prime factors can be used to form groups, find patterns, etc. 
The prime factors of 12 are 2 and 3.

Common Factors

Common factors are numbers that are factors of two or more numbers. They are helpful when we solve problems that involve multiple numbers. We use common factors while sharing resources, grouping, etc.
Let’s understand common factors with an example. 1, 2, 3, and 6 are the common factors of 12 and 18. This can be determined by identifying the factors of 12 and 18 separately. While the factors of 12 are 1, 2, 3, 4, 6, 12, the factors of 18 are 1, 2, 3, 6, 9, 18. Now, among these factors, only 1, 2, 3, and 6 can be seen in both lists. Hence, they are the common factors. 

Greatest Common Factor

The greatest common factor or GCF is the largest common factor of two or more numbers. It is also called the greatest common divisor (GCD). GCF helps simplify problems, such as reducing fractions or dividing items into groups. 
Let’s say we need to determine the GCF of 12 and 18. To find the GCF, we should first find the factors of 12 and 18. Then we can simply choose the largest common factor. 
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 18: 1, 2, 3, 6, 9, 18.
So, GCF of 12 and 18 is 6.

Difference Between Factors and Multiples

Factors Multiples Factors are the numbers that divide a given number exactly without leaving any remainder.0 Multiples are the results obtained when a number is multiplied by whole numbers. A factor of a number is always less than or equal to that number. Multiples are always equal to or greater than the given number. The number of factors for any number is finite, and they always include 1 and the number itself. A number has an infinite number of multiples.   1 is the smallest factor of every number Every number is a multiple of 1.

Tips and Tricks to Master Factors

To learn factors more quickly, use the following tips and tricks.

  • Instead of listing all the factors, find pairs of factors that help in finding the factors easily.
  • Breaking a number into prime factors helps solve many factor-related problems, such as finding the LCM and GCF.
  • Begin with 1 and test numbers successively up to the square root of the number, checking which numbers divide it evenly. Every time we find one, we should pair it with its matching factor. 
  • When finding even numbers, always remember that 2 is a factor of every even number.
  • Remember that all perfect squares have odd numbers of factors.
  • Teachers can use simple examples like finding factors of 10 (1, 2, 5, 10) to build clarity.
  • Parents can encourage kids to practice both operations since factors and multiples are connected.
  • Parents can include small games during chores to make learning fun.

Common Mistakes and How to Avoid Them in Factors

Students often make mistakes when working with factors. That’s where the below-mentioned common mistakes can be useful, as they help us learn how to avoid those mistakes.
 

Real-World Applications of Factors

Factors can be used in many fields. From accomplishing everyday tasks to solving advanced problems, factors have a wide range of applications. Let's explore some of their practical uses with examples.


Distributing items equally: Factors help with fair distribution when dividing items into groups without leaving any leftovers. For instance, it can be used in a situation where 12 candies need to be distributed equally to 6 children. This problem can be solved by dividing 12 by 6. Since 12/6 is 2, each child will get 2 candies.

Simplifying fractions: GCFs are used to simplify fractions to their lowest terms. For example, let's simplify the fraction 18/24. 

  • Factors of 18 are 1, 2, 3, 6, 9, and 18.
     
  • Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
     
  • Common factors of 18 and 24 are 1, 2, 3, and 6.
     
  •  GCF is the largest common factor.


Since 6 is the largest number among the common factors of 18 and 24, the GCF is 6.


Divide the numerator and denominator by 6.


18/24 = (18/6)/(24/6) = 3/4 


Finding patterns in sequences: Factors can be used to identify intervals in sequences or patterns that repeat. For example, if we need to plan one particular event in the next 2 days and a second event in 6 days' time, we can use LCM to determine the meeting point of the events. Since the LCM of 2 and 6 is 6, the events will merge every 6 days.

Building and construction: Factors play an essential role while constructing and building, as they can be used to find equal partitions of structures.

Tiling and flooring: Factors determine the size of tiles that can fit perfectly into a floor without gaps.

Download Worksheets

Problem 1

Find the GCF of 28 and 42.

Okay, lets begin

The GCF of 28 and 42 is 14.

Explanation

To find the GCF, list the factors of each number and choose the largest factor that is common in both the lists. 

  • Factors of 28: 1, 2, 4, 7, 14, 28.
     
  • Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42.
     
  • The common factors are 1, 2, 7, and 14.

GCF of 28 and 42 is 14.
 

Well explained 👍

Problem 2

Ram goes to music class every 3 days and Sam goes to dance class every 4 days. When will they meet?

Okay, lets begin

They meet once in every 12 days.

Explanation

To find the days when they meet, we need to find the LCM. To find LCM, we need to find the prime factors of each number and multiply the highest factors of all the prime factors.


Step 1: Prime factors of both the numbers should be found.

Prime factors of 3: 31.

Prime factors of 4: 22

Step 2: LCM can be found by multiplying the highest power of all the factors.

LCM = 22 × 31 = 12.

Therefore, they both meet every 12 days.
 

Well explained 👍

Problem 3

Find the prime factorization of 72.

Okay, lets begin

23 × 32 is the prime factorization of 72.
 

Explanation

For finding the prime factorization, we should divide the given number by the smallest prime numbers until the remainder becomes 1.

Step 1: Divide 72 by the smallest prime number 2.

72/2 = 36

Step 2: Continue dividing by 2.

36/2 = 18

Step 3: Divide by 2.

18/2 = 9

Step 4: Divide the number by the other smallest prime number 3.

9/3 = 3

Step 5: Divide it again by 3.

3/3 =  1

Hence, the prime factorization of 72 is 23 × 32.
 

Well explained 👍

Problem 4

Find the factors of 24

Okay, lets begin

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
 

Explanation

For finding factors, we need to multiply two numbers, which results in 24

Step 1: Start multiplying with 1 and 24.

1 × 24 = 24

Step 2: Check with the subsequent numbers.

2 × 12 = 24

3 × 8 = 24

4 × 6 = 24

Step 3: Stop when the factors are repeating.

6 × 4 = 24

Therefore, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
 

Well explained 👍

Problem 5

Find the smallest number divisible by 15 and 20.

Okay, lets begin

The smallest number divisible by 15 and 20 is 60.
 

Explanation

 The smallest number is the LCM of 15 and 20.

Step 1: Find the prime factorization of both numbers.

15 = 3 × 5

20 = 22 × 5

Step 2: Multiplying the highest powers of all the numbers gives the LCM.

LCM = 22 × 31 × 51 = 60
 

Well explained 👍

FAQs on Factors

1.What are factors?

Factors are numbers that divide the given number evenly without leaving any remainder.
 

2.What are the factors of 12?

1, 2, 3, 4, 6, and 12 are the factors of 12.

3.What is the smallest factor of 20?

1 is the smallest factor of 20, and it is the smallest factor of all the numbers.
 

4.Why is 1 not a prime number?

A prime number must have two factors. 1 and the number itself. 1 has only one factor, so it is not a prime.
 

5.What are prime factors?

Prime factors are factors of a number that are also prime numbers.

6.What are the factors of 24 ?

Factors of 24 are 2, 3, 4, 6, 8, 12, and 24
 

7.What are the types of factors?

The types of factors are : 

Prime factors


Composite factors


Proper factors


Improper factors


Unit factors 


Lowest common factors(LCM)


Highest common factors(HCF)
 

8.What is the difference between factors and multiples?

Factors are defined as the integers that divide a number completely without leaving any remainder. Multiples, on the other hand, are numbers that result when a number is multiplied by another whole number.
 

9.What are the first four factors of 4?

4 has only three factors: 1, 2, and 4.
 

10.What are the factors of 36 ?

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
 

Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.