Factors of 21
2026-02-28 01:12 Diff
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Last updated on December 17, 2025

Numbers whose dividend is completely divisible by quotient are its factors. In real life, factors are helpful in scenarios like packing boxes and arranging seats. In this article, we will be studying examples, mistakes, and methods to solve factors of 21.

What are the Factors of 21

The factors of 21 are 1, 3, 7 and 21


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


Negative factors: -1, -3, -7, -21

Prime Factors - Prime factors are the prime numbers themselves, when multiplied together, give 21 as the product.
Prime factor: 3, 7 

Prime Factorization- Prime factorization involves breaking 21 into its prime factors


It is expressed as 31 × 71

The factors of 21 can be written as shown in the table given below:

Factor Type Values Positive Factors of 21 1, 3, 7, 21 Negative Factors of 21 -1, -3, -7, -21 Prime Factors of 21 3, 7 Prime Factorization of 21 3 × 7 The Sum of the Factors of 21 32

How to Find the Factors of 21

There are different methods to find the factors of 21.

Methods to find the factors of 21:

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

Finding Factors Using Multiplication Method

The multiplication method finds the pair of factors that give 21 as their product.

Step-by-step process

Step 1: Find the pair of numbers whose product is 21. 


Step 2: The factors are those numbers, when multiplied, give 21.


Step 3: Make a list of numbers whose product will be 21.

A list of numbers whose products are 21 is given below:

1 × 21 = 21


3 × 7 = 21
 

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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: 21÷1 = 21


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

Overview of Factors of 21 using the division method

Prime Factors and Prime Factorization

Prime Factors of 21

Prime Factors of 21-There is only one prime factor for 21


Prime factors of 21: 3, 7

Steps to find the prime factors of 21

Step 1:  Divide 21 using the prime number 3

21÷3 = 7

Step 2: Divide 5 with the prime number 7


7÷7 = 1

Prime Factorization of 21

Prime Factorization of 21- Prime Factorization breaks down the prime factors of 21


Expressed as 31 × 71

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 21:

Factor Pairs of 21

The factors of 21 can be written in both positive and negative pairs. The table below represents the factor pairs of 21, where the product of each pair of numbers is equal to 21.

Positive Pair Factors of 21:

Factors Positive Pair Factors 1 × 21 = 21 1, 21 3 × 7 = 21 3, 7

Since the product of two negative numbers is also positive, 21 also has negative pair factors.

Negative Pair Factors of 21:

Factors Negative Pair Factors −1 × −21 = 21 −1, −21 −3 × −7 = 21 −3, −7

Common Mistakes and How to Avoid Them in Factors of 21

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

Can you express 21 as a product of two factors other than 1 and 21?

Okay, lets begin

Yes, 21 can be expressed as a product of factors 3 and 7. 
 

Explanation

When 3 is multiplied by 7 (3×7) we get 21 as the product. Other than the factors 1 and 21, we can also multiply 3 and 7 to get the product 21.
 

Well explained 👍

Problem 2

What is the sum of factors of 21?

Okay, lets begin

The sum of factors of 21 is 32
 

Explanation

Write the factors of 21 and add them together to get the sum.


The factors of 21 are 1, 3, 7 and 21. Sum of factors = 1+3+7+21 = 32

Well explained 👍

Problem 3

Identify the factor pair whose sum is 10

Okay, lets begin

The factor pair is (3,7)
 

Explanation

When the factor pair (3,7) is added (3 + 7), we get 10 as the sum.
 

Well explained 👍

Problem 4

At a Costco store in Chicago, a teacher buys 21 snack packs for a school event. She wants to arrange the packs equally into rows with no leftovers. What are all the possible numbers of packs she can place in each row?

Okay, lets begin

1, 3, 7, 21

Explanation

To arrange the snack packs evenly, we find all the factors of 21. Factors are numbers that divide 21 exactly without leaving a remainder.


21 ÷ 1 = 21
21 ÷ 3 = 7
21 ÷ 7 = 3
21 ÷ 21 = 1


So, the factors of 21 are 1, 3, 7, and 21.

Well explained 👍

Problem 5

A youth NFL football camp in Dallas orders 21 jerseys for players. The coach wants to divide the jerseys equally among groups. Which group sizes are possible without any jersey left over?

Okay, lets begin

1, 3, 7, 21

Explanation

To divide the jerseys equally, the group size must be a factor of 21.


Since 21 can be divided evenly by 1, 3, 7, and 21, these are the possible group sizes. Any other number would leave leftover jerseys.

Well explained 👍

Problem 6

A CVS pharmacy in Boston receives a shipment of 21 medicine sample packets for a school science health program. The packets must be divided equally among students. What are the possible numbers of students who can receive the packets evenly?

Okay, lets begin

1, 3, 7, 21

Explanation

To distribute the medicine packets evenly, we list the factors of 21.


Only numbers that divide 21 completely are valid. These are 1, 3, 7, and 21.


So, the packets can be shared evenly among 1, 3, 7, or 21 students.

Well explained 👍

FAQs on Factors of 21

1.Does 21 only have 2 factors?

No, there are 4 factors of 21. The factors of 21 are 1, 3, 7 and 21.
 

2.Is 21 a prime factor?

No, 21 is not a prime factor because it has more than two factors. Any number with more than two factors are composite. Hence, 21 is a composite number. The factors of 21 are 1, 3, 7 and 21.
 

3.What is the factor tree of 21?

A factor tree of 21 visually represents its prime factors as branches of the tree. The prime factors of 21 are 3 and 7.
 

4.Is 18 a factor of 21?

No, 18 is not a factor of 21 because 21 can't be completely divided by 18. When 21 is divided by 18, the remainder is not zero. Factors are numbers that can divide 21 completely.
 

5.Is 21 a factor of 28?

No, 21 is not a factor of 28 because 28 can't be completely divided by 21. When 28 is divided by 21, the remainder is not zero. Factors are numbers that can divide 28 completely.
 

6.How many factors does 21 have?

The number 21 has 4 factors. Factors are whole numbers that divide 21 evenly without leaving a remainder. These factors come in pairs that multiply to give 21.

7.What is the smallest factor of 21?

The smallest factor of 21 is 1.
This is because 1 divides every whole number evenly and is always the smallest possible factor.

8.What is the largest factor of 21?

The highest factor of 21 is 21 itself.
Every number is divisible by itself, so the largest factor of a number is always the number itself.

9.Which factors of 21 add up to 13?

The factors of 21 that add up to 13 are 3 and 10.
These two numbers add to 13, but 10 is not a factor of 21, so there are no factors of 21 that add up to 13.

10.How many even factors does 21 have?

The number 21 has 0 even factors.
This is because 21 is an odd number and is not divisible by 2, so none of its factors are even.

11.What are the odd factors of 21?

The odd factors of 21 are 1, 3, 7, and 21.
All the factors of an odd number are odd.

12.What is the sum of all the factors of 21?

The sum of all the factors of 21 is 32.


Adding all the factors together gives:
1 + 3 + 7 + 21 = 32.

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.