# What are all the factors, the prime factorization, and factor pairs of 84?

To find the factors of 84, divide 84 by each number starting with 1 and working up to 84

## Factors of Numbers similar to 84

## Introduction to Factors

Factors are the building blocks of numbers; they are the integers we multiply together to produce another number. Understanding these factors illuminates the structure and characteristics of a number within the realm of mathematics. Let’s consider **84** as an illustrative example to delve into the world of factors. Factors of **84** are the whole numbers which, when multiplied in pairs, give the product as **84**. This exploration offers insights into the makeup and properties of **84** in the mathematical landscape.

## What are Factors of 84?

The concept of factors for the number **84** revolves around identifying those integers that can evenly divide **84** without leaving a remainder. Below is a list of factors for **84** that showcases this concept clearly.

- 1
- 2
- 3
- 4
- 6
- 7
- 12
- 14
- 21
- 28
- 42
- 84

## How to Find the Factors of 84?

Discovering the factors of **84** can be achieved through the division method. This approach involves dividing **84** by integers that are less than or equal to it. The division method is depicted as follows:

- Divide 84 by 1:
**84 ÷ 1 = 84** - Divide 84 by 2:
**84 ÷ 2 = 42** - Divide 84 by 3:
**84 ÷ 3 = 28** - Divide 84 by 4:
**84 ÷ 4 = 21**

If the result of a division is a whole number, that divisor is a factor of **84**.

## Pair Factors of 84

Pair factors of **84** are two numbers which, when multiplied together, equal **84**. These can be positive or negative and are listed below:

Positive Pair Factor 1 | Positive Pair Factor 2 |
---|---|

1 | 84 |

2 | 42 |

3 | 28 |

4 | 21 |

Negative pair factors are also applicable since the multiplication of two negative numbers yields a positive product. For example, **-1 × -84 = 84**.

## Prime Factorization of 84

The prime factorization of **84** involves breaking it down into its prime factors. This can be visually represented through a factor tree, which simplifies **84** step-by-step into its prime elements.

Thus, the prime factorization of 84 is **2 × 2 × 3 × 7**, which can also be written as **2² × 3 × 7**.

## Important Points to Remember

Here are some vital points regarding the factors of **84** to keep in mind:

- Total factors: 12
- Prime factors: 2, 3, and 7
- Pair factors: Both positive and negative pair factors such as (1, 84) and (-1, -84)
- Sum of all factors: The sum of all factors of
**84**is 224.

An interesting fact about **84** is that it is both a product of a twin prime (3 and 7) and a perfect square (2²).

## Other conversions of the number 84

84 in Roman numerals

84 in Spanich

84 in Italian