# What Are Factors of 84? – Definition With Examples

Created on Dec 18, 2023

Updated on January 14, 2024

Welcome to another exciting exploration with Brighterly, where we illuminate the magical world of mathematics for children of all ages. Today, we’re venturing into the captivating realm of factors, with a special spotlight on the number 84. Have you ever thought about how numbers break apart into smaller pieces? Or wondered what hidden connections lie within the digits we use every day? At Brighterly, we believe that numbers aren’t just symbols on a page; they’re keys to unlocking a universe of knowledge, creativity, and fun. As we dive into the concept of factors, specifically looking at the number 84, we’ll be your guides through a mathematical landscape filled with intriguing patterns, puzzles, and discoveries. So buckle up, dear young mathematicians; it’s time to journey through the factors of 84, where learning math is not just educational but thrillingly bright with Brighterly!

## Understanding the Number 84

The number 84 is an interesting figure that we come across in various aspects of mathematics and everyday life. It’s an even number and has significant properties that make it a fascinating subject to explore. If you’ve ever wondered how numbers break down into smaller parts, you’ve arrived at the right place. In this guide, we will embark on an engaging journey through the world of factors, focusing on the number 84. But first, let’s take a moment to understand what factors are in the general sense.

## Definition of Factors of 84

Factors are numbers that divide another number completely, leaving no remainder. In the context of 84, the factors are numbers that divide 84 without any leftovers. For example, 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84 are all factors of 84. These numbers have a special relationship with 84, and exploring them will open a new door to understanding the rich and intricate patterns in mathematics. You can verify these factors using a simple division calculator.

## Prime Factors of 84

Among the factors of 84, some are prime numbers. A prime number is one that has only two factors: 1 and itself. For 84, the prime factors are 2, 3, and 7. This means that 84 can be expressed as a product of these prime numbers: $_{2}×3×7$. This is a vital concept, especially when we delve into more complex mathematical ideas like the Greatest Common Divisor (GCD).

## Composite Factors of 84

Along with prime factors, there are also composite factors of 84. Composite numbers are those that have more than two factors. In the case of 84, the composite factors include 4, 6, 12, 14, 21, 28, and 42. These numbers are not prime, as they can be further divided into smaller factors.

## Properties of Factors of 84

The factors of 84 have several intriguing properties. They can be categorized into even and odd, or prime and composite. Additionally, the sum of all these factors equals 224, and the product of the factors taken two at a time provides insight into deeper mathematical relationships. This exploration showcases the fascinating world of numbers that often goes unnoticed.

## Properties of Prime Factors

Prime factors have their own unique characteristics. They are the building blocks of numbers and represent the essence of multiplication and division. Understanding prime factors is like cracking the code to how numbers work. They have applications in cryptography, computer science, and are central to the Fundamental Theorem of Arithmetic.

## Properties of Composite Factors

Composite factors, in contrast, add complexity to our understanding of numbers. They exhibit patterns and relationships that make numbers engaging and enjoyable to study. Whether it’s their role in divisibility rules or their connection to geometric shapes, composite factors bring numbers to life in unexpected ways.

## Difference Between Prime and Composite Factors of 84

The difference between prime and composite factors of 84 is fundamental. Prime factors are indivisible, while composite factors can be broken down further. In the context of 84, this distinction helps in understanding not just the number itself, but a broader spectrum of mathematical concepts.

## Methods to Find the Factors of 84

### Using Division

Finding the factors of 84 using division is a straightforward method. By dividing 84 by every integer from 1 to 84 and checking for a remainder of zero, we can identify all the factors.

### Using Prime Factorization

Another efficient method is using prime factorization. By breaking down 84 into its prime factors (as mentioned earlier), we can find all the factors through combinations of those primes.

## Practice Problems on Finding the Factors of 84

Ready to test your knowledge? Here are some practice problems:

- List all the even factors of 84.
- Identify the prime factors of 84.
- Find the largest composite factor of 84.

Work on these problems and check your answers with reliable math resources.

## Conclusion

As we conclude this enlightening journey through the world of factors, we hope that you’ve discovered the joy, beauty, and sheer wonder that numbers hold. At Brighterly, we strive to make learning mathematics a thrilling experience, turning ordinary numbers into extraordinary explorations. Understanding the factors of 84 has been more than an academic exercise; it’s been a gateway to a universe of knowledge that’s as vast and limitless as your imagination. By now, you should have a strong grasp of prime and composite factors, and how they intricately weave together to form the number 84. But remember, the adventure doesn’t end here. With Brighterly by your side, there are endless opportunities to explore, learn, and grow. Keep questioning, keep exploring, and keep shining brightly with Brighterly!

## Frequently Asked Questions on Factors of 84

### What are the factors of 84?

The factors of 84 are numbers that evenly divide 84 without a remainder. Specifically, they are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. These numbers have a unique relationship with 84, allowing for various mathematical explorations and insights.

### Why are prime factors important?

Prime factors play a crucial role in mathematics because they are the fundamental building blocks of numbers. They enable us to understand the structure of numbers, simplify complex mathematical operations, and have applications in fields ranging from cryptography to computer science. With Brighterly, we encourage curiosity about prime factors as they lead to an enriched understanding of the numerical world around us.

### How can I find the factors of a number?

Finding the factors of a number can be achieved through several methods, such as division and prime factorization. Division involves dividing the number by each integer from 1 to itself, checking for a remainder of zero. Prime factorization breaks the number down into its prime constituents, allowing for an understanding of its composite structure. These methods, when practiced with Brighterly’s engaging tools and resources, make the process of finding factors both intuitive and enjoyable.