100 LearnersLast updated on May 26th, 2025
Factors of 1684
Factors are the numbers that divide any given number evenly without a 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 1684, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1684?
The numbers that divide 1684 evenly are known as factors of 1684.
A factor of 1684 is a number that divides the number without remainder.
The factors of 1684 are 1, 2, 4, 421, 842, and 1684.
Negative factors of 1684: -1, -2, -4, -421, -842, and -1684.
Prime factors of 1684: 2 and 421.
Prime factorization of 1684: 2² × 421.
The sum of factors of 1684: 1 + 2 + 4 + 421 + 842 + 1684 = 2954
How to Find Factors of 1684?
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 1684. Identifying the numbers which are multiplied to get the number 1684 is the multiplication method.
Step 1: Multiply 1684 by 1, 1684 × 1 = 1684.
Step 2: Check for other numbers that give 1684 after multiplying
2 × 842 = 1684
4 × 421 = 1684
Therefore, the positive factor pairs of 1684 are: (1, 1684), (2, 842), and (4, 421).
All these factor pairs result in 1684.
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 result as whole numbers as factors. Factors can be calculated by following a simple division method:
Step 1: Divide 1684 by 1, 1684 ÷ 1 = 1684.
Step 2: Continue dividing 1684 by the numbers until the remainder becomes 0.
1684 ÷ 1 = 1684
1684 ÷ 2 = 842
1684 ÷ 4 = 421
Therefore, the factors of 1684 are: 1, 2, 4, 421, 842, 1684.
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 1684 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1684 ÷ 2 = 842
842 ÷ 2 = 421
421 ÷ 421 = 1
The prime factors of 1684 are 2 and 421.
The prime factorization of 1684 is: 2² × 421.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1684 is divided by 2 to get 842.
Step 2: Now divide 842 by 2 to get 421. Here, 421 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1684 is: 2² × 421.
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 1684: (1, 1684), (2, 842), and (4, 421).
Negative factor pairs of 1684: (-1, -1684), (-2, -842), and (-4, -421).
Common Mistakes and How to Avoid Them in Factors of 1684
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1684, 1 and 1684 are also factors.
Factors of 1684 Examples
Problem 1
There are 1684 apples and 4 baskets. How many apples will each basket contain if distributed equally?
Each basket will contain 421 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of baskets.
1684/4 = 421
Problem 2
A rectangular garden has a length of 421 meters and a total area of 1684 square meters. What is the width?
4 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1684 = 421 × width
To find the value of width, we need to shift 421 to the left side.
1684/421 = width
Width = 4.
Problem 3
There are 842 pieces of candy and 2 children. How many candies will each child receive?
Each child will receive 421 candies.
Explanation
To find the candies each child will receive, divide the total candies by the number of children.
842/2 = 421
Problem 4
A group of 1684 students is divided into 2 classes. How many students are there in each class?
There are 842 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
1684/2 = 842
Problem 5
1684 books need to be arranged in 1 shelf. How many books will go on the shelf?
The shelf will have 1684 books.
Explanation
Divide total books by the number of shelves.
1684/1 = 1684
FAQs on Factors of 1684
1.What are the factors of 1684?
2.Mention the prime factors of 1684.
3.Is 1684 a multiple of 4?
4.Mention the factor pairs of 1684.
5.What is the square of 1684?
Important Glossaries for Factor of 1684
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1684 are 1, 2, 4, 421, 842, and 1684.
- Prime factors: The factors which are prime numbers. For example, 2 and 421 are prime factors of 1684.
- 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 1684 are (1, 1684), (2, 842), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1684 is 2² × 421.
- Multiple: A multiple of a number is the product of that number and an integer. For example, 1684 is a multiple of 4.
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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.
