Factors of 108: Chart, Factor Pairs, and Step-by-Step Calculation
Factors of 108 are all the numbers that are divisible into 108 without any remainders. These factors are whole numbers and can be both positive and negative. In this page, we will learn how to find out all the factors of 108, including prime factors of 108.
The answer of :
- Factors of 108 are : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- Prime Factors of 108 : 2, 3
How to Find Factors of 108: A Step-by-Step Mathematical Approach
What are the factors of 108? The factors of 108 are the whole numbers 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. As a Ministry-inspected school, Queen Elizabeth Academy emphasizes a foundations-first approach to understanding number properties: a factor is any integer that divides into 10 evenly with zero remainder. In this guide, OCT-certified educators break down how to identify factor pairs, calculate the prime factorization of 108 ( ), and understand their applications in higher-level algebra.
- Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- Prime Factors of 108: 2, 3
- Prime Factorization:
How to Find Factors of 108: A Step-by-Step Mathematical Approach
At Queen Elizabeth Academy, we teach factorization as the process of breaking a number down into its "building blocks." Understanding how to factor 108 is a core competency in the Ontario Grade 6-8 curriculum, serving as the foundation for more advanced topics like Greatest Common Factor (GCF) and algebraic fractions.
To factor 108 effectively, our OCT-certified instructors recommend the Division Method:
Start with 1: Every integer is divisible by 1. Since , both 1 and 108 are factors.
Check 2: Since 108 is an even number, it is divisible by 2. , making 2 and 54 a factor pair.
Test 3 and 4: and . Both are whole numbers, adding (3, 36) and (4, 27) to our list.
Reach the Square Root: Once you reach the number's square root (approximately 10.39 for 108), you have found all unique pairs.
By mastering these fundamental building blocks, students transition from rote memorization to conceptual mastery, a key pillar of the QEA educational methodology.
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Table of Contents :
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Pair Factors of 108
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Prime Factorization of 108 (Step-by-Step)
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Factor Pairs of 108 Explained
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How to Calculate Factors: The Division Method
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Real-World Examples & Practice Problems
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FAQ: Common Questions About Factoring 108
Pair Factors of 108
In order to get the pair factors, we need to find two numbers multiplied together can get 108.
Multiplication
1 x 108
2 x 54
3 x 36
4 x 27
6 x 18
9 x 12
Positive pair
factors of 108
(1, 108)
(2, 54)
(3, 36)
(4, 27)
(6, 18)
(9, 12)
Negative pair
factors of 108
(-1, -108)
(-2, -54)
(-3, -36)
(-4, -27)
(-6, -18)
(-9, -12)
Prime Factorization of 108 (Step-by-Step)
To obtain the prime factors of 108, you need to find the factors of 108 and divide them out.
- 108 divided by 2 is 54
- Then if you keep dividing 54
- You get the final breakdown of the 108 = 2 × 2 × 3 × 3 × 3
Prime Factorization of 108
To determine the prime factors of 108, we use the process of prime factorization to break the composite number down into its most basic building blocks.
- Step 1: Since 108 is an even number, we begin by dividing by the smallest prime number, 2.
- Step 2: . Since 54 is even, we divide by 2 again: .
- Step 3: Since 27 is odd, we move to the next prime number, 3. , and . Since 3 is a prime number, our factorization is complete.
The Prime Factors of 108 are 2 and 3.
The Prime Factorization Equation
Using the foundations-first method taught at Queen Elizabeth Academy, we express the final breakdown as:
Teacher’s Tip: Always remember that while 1 is a factor of 108, it is not a prime number. Therefore, it is never included in a prime factor tree or a prime factorization equation.
To find out more factors:
How to Calculate Factors: The Division Method
To identify the factors of any number, we use the Division Method. Factors are strictly integers (whole numbers). If you divide 108 by a number and the result has no remainder, that number is a factor.
The Step-by-Step Calculation
Our educators at Queen Elizabeth Academy recommend testing divisors sequentially:
(No remainder; 1 is a factor)
(No remainder; 2 is a factor)
with a remainder of 3 (5 is not a factor)
Practice Examples: Finding Common Factors
At Queen Elizabeth Academy, we teach students that finding common factors is the essential first step to simplifying fractions. Here are three examples involving the number 108.
1. Find the common factors of 108 and 12
Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 12: 1, 2, 3, 4, 6, 12
Answer:
The common factors are 1, 2, 3, 4, 6, and 12. (The Greatest Common Factor is 12).
2. Find the common factors of 108 and 25
Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 25: 1, 5, 25
Answer:
The only common factor is 1.
Expert Note:
When two numbers only share the common factor of 1, they are called "Relatively Prime."
3. Find the common factors of 108 and 54
Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Answer:
The common factors are 1, 2, 3, 6, 9, 18, 27, and 54.
FAQ: Frequently Asked Questions About the Factors of 108
What are the factors of 108?
The factors of 108 are the integers that divide 108 exactly without leaving a remainder. There are 12 positive factors in total: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
What are the multiples of 108?
Multiples are the result of multiplying 108 by any whole number. Unlike factors, which are finite, multiples are infinite. The first five multiples are 108, 216, 324, 432, and 540.
Is 108 a prime or composite number?
108 is a composite number. By definition, a prime number has only two factors (1 and itself). Since 108 can be divided evenly by 12 different numbers, it is composite. It is also an even number, and every even number greater than 2 is composite.
How many prime factors does 108 have?
There are two unique prime factors for 108: 2 and 3. Through the process of prime factorization, 108 is broken down into these prime components:
This can also be written using exponents as:
What is a "Proper Factor" of 108?
A proper factor is any factor of a number excluding the number itself. For 108, the proper factors are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, and 54.
The sum of the proper factors of 108 is 172
(). Because this sum is greater than the number 108, 108 is classified as an abundant number in number theory.
Can factors of 108 be negative?
Yes. In advanced algebra, we acknowledge that factors can be negative because the product of two negative integers is a positive integer. The negative factors of 108 are -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, and -108. In many standard math curriculum applications, however, the focus remains primarily on positive integers.
