Factors of 10
2026-02-28 10:14 Diff
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Last updated on December 11, 2025

The factors of 10 are whole numbers and they are finite. These factors divide 10 completely, leaving zero as the remainder. In real life, we use factors for calculating the dimensions needed for structures in engineering. In this article, you will learn more about the factors of 10.

What are the Factors of 10

The factors of 10 are 1, 2, 5 and 10


Negative Factors: These are negative counterparts of the positive factors.


Negative factors: -1, -2, -5, -10

Prime Factors:Prime factors are the prime numbers themselves, when multiplied together, give 10 as the product.


Prime factor: 2, 5 

Prime Factorization: Prime factorization involves breaking 10 into its prime factors


It is expressed as 21 × 51

Table listing the factors of 10:

Positive Factors

1, 2, 5, 10

Negative Factors

-1, -2, -5, -10

Prime Factors

 2,5

Prime Factorization

21 × 51

How to Find the Factors of 10

There are different methods to find the factors of 10.

Methods to find the factors of 10:

  • Multiplication Method
  • Division Method
  • Prime Factor and Prime Factorization
  • Factor Tree
     

Finding Factors Using Multiplication Method

The multiplication method finds the pair of factors that give 10 as their product. Step-by-step process given below:

Step 1: Find the pair of numbers whose product is 10. 


Step 2: The factors are those numbers, when multiplied, give 10.


Step 3: Make a list of numbers whose product will be 10.

A list of numbers whose products are 10 is given below:

  • 1 × 10 = 10
  • 2 × 5 = 10

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Finding Factors Using Division Method

The division method finds the numbers that fully divide the given number. Step-by-step process given below:

Step 1: Since every number is divisible by 1, 1 will always be a factor.  Example: 10÷1 = 10


Step 2: Move to the next integer. Both divisor and quotient are the factors. 

Picture showing the division method:

Overview of Factors of 10 using the division method:

Prime Factors and Prime Factorization

Multiplying prime numbers to get the given number as their product is called prime factors. Prime factorization is breaking down the number into its prime factors.

Prime Factors of 10: There are two prime factors for 10


Prime factors of 10: 2, 5

Step 1:  Divide 10 using the prime number 2

10÷2 = 5

Step 2: Divide 5 with the prime number 5


5÷5 = 1


Prime Factorization of 10: Prime Factorization breaks down the prime factors of 10


Expressed as 21 × 51

Factor Tree

The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.


Factor Tree for 10:

Factors of 10 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.

 
Positive Factor Pairs: (1,10), (2,5)


Negative Factor Pairs:  (-1,-10), (-2,-5)

Common Mistakes and How to Avoid Them in Factors of 10

Mistakes can occur while finding the factors. Learn about the common errors that can occur. Solutions to solve the common mistakes are given below.

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Problem 1

Product of odd factors of 10

Okay, lets begin

 The product is 5
 

Explanation

The odd factors of 10 are 1 and 5. When these odd factors are multiplied (1×5), we get 5 as the product.
 

Well explained 👍

Problem 2

Find the sum of factors of 10 and check if it's a multiple of 9

Okay, lets begin

The sum is 18, and it is a multiple of 9
 

Explanation

 List the factors of 10 and add them to get 18 as the sum (1+2+5+10)
When 9 is multiplied by 2 we get 18 as the product, hence 18 is a multiple of 9.
 

Well explained 👍

Problem 3

Find the GCF of 10 and 100

Okay, lets begin

The GCF is 10
 

Explanation

To find the GCF, write the factors of 10 and 100 and identify the greatest common factor.


The factors of 10 are 1, 2, 5 and 10


The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100


The GCF is 10
 

Well explained 👍

Important Glossaries for Factors of 10

  • Divisor:  Number that divides another number
  • Quotient: The number you get when you divide a number with another.
  • Factor Tree: A tree diagram used to represent the prime factors of a given number
  • Factors: Numbers that divide the given number, leaving zero as the remainder.
  • Prime Factorization: Process of breaking down the prime factors.
  • GCF: Greatest Common Factor is the largest possible number seen in two or more numbers.

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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.