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How to Find Factors of 84?
To find the factors of 84, you can follow these steps:
- List the Divisors: Begin by listing the possible divisors of 84. Divisors are the numbers that divide evenly into the given number without leaving a remainder.
- Start Dividing: Divide 84 by each of the listed divisors and check if the division results in a whole number (no remainder).
- Identify Factors: The numbers that successfully divide 84 without leaving a remainder are its factors.
Here’s a breakdown of the process:
- Divisors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Testing the Divisors:
- 84 ÷ 1 = 84
- 84 ÷ 2 = 42
- 84 ÷ 3 = 28
- 84 ÷ 4 = 21
- 84 ÷ 6 = 14
- 84 ÷ 7 = 12
- 84 ÷ 12 = 7
- 84 ÷ 14 = 6
- 84 ÷ 21 = 4
- 84 ÷ 28 = 3
- 84 ÷ 42 = 2
- 84 ÷ 84 = 1
- Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
These are the factors of 84. They are the numbers that can be multiplied together to give the result of 84.
What are Factors?
Factors are the whole numbers that can be multiplied together to give a specific number as the product. In other words, factors are the numbers that divide another number evenly without leaving a remainder.
For example, let’s consider the number 12:
- The factors of 12 are 1, 2, 3, 4, 6, and 12.
- These numbers can be multiplied in various combinations to give the product 12:
- 1 × 12 = 12
- 2 × 6 = 12
- 3 × 4 = 12
In this case, 1, 2, 3, 4, 6, and 12 are all factors of 12 because they can divide 12 without any remainder.
Prime numbers, on the other hand, have only two factors: 1 and the number itself. For example, the factors of 23 are 1 and 23, because 23 is a prime number.
Understanding factors is important in various mathematical operations, such as simplifying fractions, finding common denominators, and solving equations.
What are Prime Numbers?
Prime numbers are positive integers greater than 1 that have exactly two distinct positive divisors: 1 and the number itself. In other words, prime numbers are numbers that are only divisible by 1 and themselves, and they have no other positive divisors.
For example, let’s consider the number 7:
- The factors of 7 are 1 and 7.
- Since 7 has only two factors, it is a prime number.
Prime numbers play a fundamental role in number theory and mathematics. They are the building blocks of all positive integers, and any positive integer greater than 1 can be uniquely expressed as a product of prime numbers raised to certain powers. This is known as the prime factorization.
Some examples of prime numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, and so on. It’s important to note that 2 is the only even prime number, as all other even numbers are divisible by 2 and thus have more than two divisors.
How to Find Factors of a Number?
To find the factors of a number, follow these steps:
- List Divisors: Begin by listing the possible divisors of the given number. Divisors are the whole numbers that can divide the given number without leaving a remainder.
- Start Dividing: Divide the given number by each of the listed divisors and check if the division results in a whole number (no remainder).
- Identify Factors: The numbers that successfully divide the given number without leaving a remainder are its factors.
Here’s a step-by-step breakdown:
Let’s find the factors of the number 24:
- List Divisors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Start Dividing:
- 24 ÷ 1 = 24
- 24 ÷ 2 = 12
- 24 ÷ 3 = 8
- 24 ÷ 4 = 6
- 24 ÷ 6 = 4
- 24 ÷ 8 = 3
- 24 ÷ 12 = 2
- 24 ÷ 24 = 1
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
These are the factors of 24. They are the numbers that can be multiplied together to give the result of 24.
Keep in mind that prime numbers have only two factors: 1 and the number itself. For example, the factors of 17 are 1 and 17, as 17 is a prime number.
What is Prime Factorization?
Prime Factorization is a mathematical process of breaking down a number into its prime factors. Prime factors are the individual numbers that make up a larger number when multiplied together.
What are the Practical Applications of the Factorization Equations in Our Day-to-Day Lives?
Some practical applications of the factorization equations in our day-to-day lives include:
- Finding the greatest common divisor (GCD) of two or more numbers
- Finding the prime factors of a number
- Finding the least common multiple (LCM) of two or more numbers
- Breaking a number down into its individual prime factors
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Frequently Asked Questions (FAQs) on Factors of 84
What are the factors of 84?
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
How do you find factors of 84?
Factors of 84 are the numbers that divide it without leaving a remainder. You can test divisibility by trying division with numbers from 1 to 84.
What's the significance of factors of 84?
Factors of 84 help us understand the number's divisibility properties, relationships with other numbers, and how it can be expressed as a product of prime factors.
Is 84 a prime number?
No, 84 is not a prime number. It has multiple factors other than 1 and itself.
Can the factors of 84 be grouped in pairs?
Yes, factors of non-perfect square numbers like 84 can be paired up. For example, 1 and 84, 2 and 42, 3 and 28, and so on.
Are prime numbers factors of 84?
Prime factors are prime numbers that divide a given number. While prime numbers are factors of 84, 84 itself is not a prime number.
How are factors of 84 related to its multiples?
The factors of 84 are the numbers that divide it evenly, while multiples are obtained by multiplying 84 by various whole numbers.
How do factors of 84 contribute to number theory?
Factors play a role in number theory, helping us explore properties of integers, divisibility rules, and relationships between numbers.
