Factors of 15
2026-02-28 17:42 Diff
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Last updated on December 11, 2025

Do you know what factors are? The factors are the pair of numbers that divide the given number without any remainder. Hence, we can say that the factors of 144 divide 144 without any remainder. In real life, factors are helpful in scenarios like packing boxes and arranging seats. In this article, you will learn more about the factors of 15.

What are the Factors of 15

The factors of 15 are 1, 3, 5 and 15


Negative Factors: Each positive factor will have a negative counterpart.


Negative factors: -1, -3, -5, -15

Prime Factors: These are the prime numbers, which when multiplied together give 15 as the product


Prime factor: 3, 5 

Prime Factorization: Prime factorization involves breaking 15 into its prime factors and expressing them in exponential form.


It is expressed as 31 × 51

Table listing the factors of 15
 

How to Find the Factors of 15

It is easy to find the factors of a number. We can identify the factors of 15 with the help of the methods mentioned below.

Methods to find the factors of 15:

  • 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 15 as their product.

Step-by-step process

Step 1: Find the pair of numbers whose product is 15. 


Step 2: The factors are those numbers, when multiplied, give 15.


Step 3: Make a list of numbers whose product will be 15.

A list of numbers whose products are 15 is given below:

1 × 15 = 15


3 × 5 = 15

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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

Step 1: Since every number is divisible by 1, 1 will always be a factor.  Example: 15÷1 = 15


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

Overview of Factors of 15 using the division method

Prime Factors and Prime Factorization

Prime factors of 15: 3, 5

Steps to find the prime factors of 15

Step 1:  Divide 15 using the prime number 3

15÷3 = 5

Step 2: Divide 5 with the prime number 5


5÷5 = 1


Prime Factorization of 15:

Prime Factorization breaks down the prime factors of 15


Expressed as 31 × 51
 

Factor Tree

The prime factors gets visually represented in factor tree. It shows us how the prime factors are being split into branches. 


Factor Tree for 15:
 

Factors of 15 can be written in both positive pairs and negative pairs. Their product will be equal to the number given.

 
Positive Factor Pairs: (1,15), (3,5)


Negative Factor Pairs:  (-1,-15), (-3,-5)
 

Common Mistakes and How to Avoid Them in Factors of 15

While learning the factors of 15, it is possible to commit mistakes. You can avoid making these mistakes by being more careful in the area mentioned below.
 

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Problem 1

Product of odd factors of 15

Okay, lets begin

The product is 225
 

Explanation

The odd factors of 15 are 1, 3, 5 and 15. When these odd factors are multiplied (1×3×5×15), we get 225 as the product.
 

Well explained 👍

Problem 2

Find the GCF of 15 and 45

Okay, lets begin

The GCF of 15 and 45 is 15
 

Explanation

To find the GCF, write the factors of 15 and 45 and identify the greatest common factor.


The factors of 15 are 1, 3, 5 and 15


The factors of 45 are 1, 3, 5, 9, 15 and 45


The GCF is 15
 

Well explained 👍

Problem 3

Can you find the sum of factors 3 and 5 of 15? Also, check if it is divisible by 2

Okay, lets begin

The sum of factors 3 and 5 is 8, which is divisible by 2
 

Explanation

Adding the factors 3 and 5 gives us 8 as a sum (3+5=8). To check if it's divisible by 2, see if the remainder is zero. When 8 is divided by 2, we get zero as the remainder and the quotient is 4.

Well explained 👍

FAQs on Factors of 15

1.What are the factors of negative 15?

The negative factors of 15 are  -1, -3, -5, -15. These are the negative counterparts of the positive factors of 15. The positive factors of 15 are 1, 3, 5, 15.
 

2.What is the factor tree of 15?

A factor tree of 15 visually represents its prime factors as branches of the tree. The prime factors of 15 are 3 and 5.
 

3.Is 12 a factor of 15?

No, 12 is not a factor of 15 because we cannot divide 15 completely by 12. Factors are numbers that can divide the number completely.
 

4.Is 2 a factor of 15?

No, 2 is not a factor of 15 because 15 is not completely divisible by 2. Factors are whole numbers that divide the given number completely.
 

5.Is 15 prime or composite?

15 is a composite number because it has more than two factors. The factors of 15 are 1, 3, 5 and 15. Prime numbers are numbers with two factors, 1 and the number itself.
 

Important Glossaries for Factors of 15

  • Divisor:  Number that divides another number
  • Prime Factor: A prime number having 1 and the number itself as factors.
  • Prime Factorization: Process of breaking down the prime factors and expressing them in exponential form.
  • 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.