108 LearnersLast updated on May 26th, 2025
Factors of 684
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 684, how they are used in real life, and tips to learn them quickly.
What are the Factors of 684?
The numbers that divide 684 evenly are known as factors of 684. A factor of 684 is a number that divides the number without remainder.
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 19, 36, 57, 76, 114, 171, 228, 342, and 684.
Negative factors of 684: -1, -2, -3, -4, -6, -9, -12, -19, -36, -57, -76, -114, -171, -228, -342, and -684.
Prime factors of 684: 2, 3, and 19.
Prime factorization of 684: (22 * 32 *19).
The sum of factors of 684: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 19 + 36 + 57 + 76 + 114 + 171 + 228 + 342 + 684 = 1764
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
How to Find Factors of 684?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 684. Identifying the numbers which are multiplied to get the number 684 is the multiplication method.
Step 1: Multiply 684 by 1, 684 × 1 = 684.
Step 2: Check for other numbers that give 684 after multiplying
2 × 342 = 684
3 × 228 = 684
4 × 171 = 684
6 × 114 = 684
9 × 76 = 684
12 × 57 = 684
19 × 36 = 684
Therefore, the positive factor pairs of 684 are: (1, 684), (2, 342), (3, 228), (4, 171), (6, 114), (9, 76), (12, 57), (19, 36).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which results as whole numbers as factors. Factors can be calculated by following simple division method
Step 1: Divide 684 by 1, 684 ÷ 1 = 684.
Step 2: Continue dividing 684 by the numbers until the remainder becomes 0.
684 ÷ 1 = 684
684 ÷ 2 = 342
684 ÷ 3 = 228
684 ÷ 4 = 171
684 ÷ 6 = 114
684 ÷ 9 = 76
684 ÷ 12 = 57
684 ÷ 19 = 36
Therefore, the factors of 684 are: 1, 2, 3, 4, 6, 9, 12, 19, 36, 57, 76, 114, 171, 228, 342, 684.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 684 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
684 ÷ 2 = 342
342 ÷ 2 = 171
171 ÷ 3 = 57
57 ÷ 3 = 19
19 ÷ 19 = 1
The prime factors of 684 are 2, 3, and 19.
The prime factorization of 684 is: (22 * 32* 19).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 684 is divided by 2 to get 342.
Step 2: Now divide 342 by 2 to get 171.
Step 3: Then divide 171 by 3 to get 57.
Step 4: Divide 57 by 3 to get 19. Here, 19 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 684 is: (22 * 32*19).
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 684: (1, 684), (2, 342), (3, 228), (4, 171), (6, 114), (9, 76), (12, 57), (19, 36).
Negative factor pairs of 684: (-1, -684), (-2, -342), (-3, -228), (-4, -171), (-6, -114), (-9, -76), (-12, -57), (-19, -36).
Common Mistakes and How to Avoid Them in Factors of 684
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 684, 1 and 684 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 684 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 684/1.5 = 456, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 684 are prime numbers.
For example, 2, 3, and 19 are the prime factors of 684, but it has other factors like 4, 12.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 684 as \(2^2 \times 3^2 \times 19\) and missing all the key factors.
Level Up with a Math Certification!
2X Faster Learning (Grades 1-12)
Factors of 684 Examples
Problem 1
A farmer wants to distribute 684 apples equally among 12 baskets. How many apples will each basket contain?
Each basket will contain 57 apples.
Explanation
To distribute the apples equally, divide the total apples by the number of baskets.
684/12 = 57
Problem 2
A rectangular garden has a length of 19 meters and a total area of 684 square meters. Find the width.
36 meters.
Explanation
To find the width of the garden, use the formula,
Area = length × width
684 = 19 × width
To find the value of width, divide 684 by 19.
684/19 = width
Width = 36.
Problem 3
There are 342 cookies to be packed equally into 9 bags. How many cookies will be in each bag?
Each bag will have 38 cookies.
Explanation
To find the cookies in each bag, divide the total cookies by the number of bags.
342/9 = 38
Problem 4
A school has 684 students and wants to form 114 equal-sized groups. How many students will be in each group?
There will be 6 students in each group.
Explanation
Dividing the students by the total groups will give the number of students in each group.
684/114 = 6
Problem 5
684 books need to be organized equally across 57 shelves. How many books will go on each shelf?
Each shelf will have 12 books.
Explanation
Divide total books by shelves.
684/57 = 12
Turn your child into a math star!
#1 Math Hack Schools Won't Teach!
FAQs on Factors of 684
1.What are the factors of 684?
2.Mention the prime factors of 684.
3.Is 684 a multiple of 4?
4.Mention the factor pairs of 684.
5.What is the square of 684?
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
Important Glossaries for Factors of 684
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 684 are 1, 2, 3, 4, 6, 9, 12, 19, 36, 57, 76, 114, 171, 228, 342, and 684.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 19 are prime factors of 684.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 684 are (1, 684), (2, 342), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 684 is (22* 32* 19).
- Multiple: A multiple is the result of multiplying a number by an integer. For example, 684 is a multiple of 4.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of 684
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
