Factors of 84
2026-02-28 15:49 Diff
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Last updated on December 11, 2025

The number that completely divides 84 are the factors of 84. So in daily life, factors are used in distributing teams in groups. Sometimes, for recipe, cooks apply the methods of factors for proper adjustments of ingredients.

What are the Factors of 84

The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84.


Negative Factors


Every positive factor will have a corresponding negative factor.


Negative factors: -1, -2, -3, -4, -6, -7, -12, -14, -21, -28,  -42, -84

Prime Factors


These are the prime numbers that can only be divided by 1 and the number itself.


Prime factor: 2, 3, 7

Prime Factorization


Prime factorization involves expressing the product of prime factors in exponential form.


It is expressed as 22 × 31 × 71

How to Find the Factors of 84

We can use various methods to find the factors of 84. Below, listed are the methods to find the factors:

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

Finding Factors Using Multiplication Method

The multiplication method is used to find the pair of factors whose product will be as the same as the number given.

Step-by-step process

Step 1: Find the pair of numbers whose product is 84. 


Step 2: The factors are those numbers, when multiplied, give 84.


Step 3: Make a list of numbers whose product will be 84.

A list of numbers whose products are 84 is given below:

  • 1 × 84 = 84
  • 2 × 42 = 84
  • 3 × 28 = 84
  • 4 × 21 = 84
  • 6 × 14 = 84
  • 7 × 12 = 84
     

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Finding Factors Using Division Method

The division method finds the factors that can divide 84 and leave zero as the remainder.

Step-by-step process

Step 1:Always start the division with 1 since 1 is the smallest factor of any given number.  Example: 84÷1 = 84


Step 2: Move to the next integer. Continue this process until you can’t divide 84 anymore.

Overview of Factors of 84 using the division method

Prime Factors and Prime Factorization

Prime factorization is the method of expressing the product of factors in its exponential form. The prime numbers are numbers that can be divided by 1 and the number itself.

Prime Factors of 84


There are two prime factors of 84


Prime factors of 84: 2, 3, 7

Steps to find the prime factors of 84

Step 1:  Divide 84 using the prime number 2

84÷2 = 42


42÷2= 21

Step 2: Divide 21 with the prime number 3


21÷3 = 7

Step 3: Divide 7 with the prime number 7


7÷7 = 1

Prime Factorization of 84

Prime factorization of 84 is the process of expressing the prime factors of 84 using exponents.


Expressed as 22 × 31 × 71

Factor Tree

The prime factorization is visually represented using the factor tree.

Factor Tree for 84:

Here, the given number 84, the prime factors and the composite factors of 84 are shown in different shades of green.


Factors of 84 can be written in both positive pairs and negative pairs. Their product will be equal to the number given.

 
Positive Factor Pairs: (1,84), (2,42), (3,28), (4,21), (6,14), (7,12)


Negative Factor Pairs:  (-1,-84), (-2,-42), (-3,-28), (-4,-21), (-6,-14), (-7,-12)
 

Common Mistakes and How to Avoid Them in Factors of 84

For children, it is very usual to make mistakes while solving factors. Few below are the mentioned mistakes to avoid - 
 

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Problem 1

Can you express 84 as a perfect square?

Okay, lets begin

No, 84 cannot be expressed as a perfect square.
 

Explanation

A perfect square is a number we get when the same number is multiplied twice. To get 84 as the product, we can multiply number together, whose product is 84. The numbers whose product is 84 are: (1 × 84), (2 × 42), (3 × 28), (4 × 21),
 (6 × 14), (7 × 12)
 

Well explained 👍

Problem 2

Identify the multiples of 3 from the factors of 84

Okay, lets begin

 The multiples of 3 from the factors of 84 are 3, 6, 12, 21, 42 and 84

Explanation

Multiples are numbers we get when another number multiplies the given number. Here, multiples of 3 are numbers we get when 3 is multiplied by another. 


The multiples of 3 from factors of 84 are 3 (1×3), 6 (2×3), 12 (4×3), 21 (7×3), 
42 (14×3), 84 (28×3)
 

Well explained 👍

Problem 3

Verify whether 84 is a multiple of 4

Okay, lets begin

Yes, 84 is a multiple of 4
 

Explanation

Multiples of 4 are numbers we get when 4 is multiplied by another number. When 4 is multiplied by 21, we get 84 as the product(4×21=84).
 

Well explained 👍

FAQs on Factors of 84

1.What is the greatest factor of 84?

The greatest factor of 84 is 84. For any number, the greatest factor will always be the given number itself.
 

2.What are the prime factors of 84?

The prime factors of 84 are 2, 3, and 7. Prime factors are the prime numbers themselves. The prime numbers are numbers with two factors, 1 and the number itself.
 

3.What is not a factor of 84?

Numbers that cannot divide 84 completely can’t be a factor of 84. For example, 5, 8, 10, and 86 can never be factors of 84
 

4.What is the sum of odd factors of 84?

The sum is 32. Odd factors are numbers that are not divisible by 2. The odd factors of 84 are 1, 3, 7 and 21. When these odd factors are added, we get 32 as the sum.
 

5.How many composite factors does 84 have?

There are 8 composite factors. These are numbers having more than two factors. The composite factors of 84 are 4, 6, 12, 14, 21, 28, 42 and 84

Important Glossaries for Factors of 84

  • Whole Number: Numbers starting from zero.
  • Quotient: It is the number that gets as a result of division
  • Factors: Numbers that divide the given number completely without any remainder.
  • Prime Factors: Prime numbers that multiply together to form the given number.
  • Prime Factorization: Process of breaking down the number into prime factors
  • Negative Factors: These are negative counterparts of the positive factors.
     

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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.