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

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
   

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
   

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 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

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)
 

• 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.