110 LearnersLast updated on May 26th, 2025
Factors of 830
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 830, how they are used in real life, and tips to learn them quickly.
What are the Factors of 830?
The numbers that divide 830 evenly are known as factors of 830. A factor of 830 is a number that divides the number without remainder. The factors of 830 are 1, 2, 5, 10, 83, 166, 415, and 830.
Negative factors of 830: -1, -2, -5, -10, -83, -166, -415, and -830.
Prime factors of 830: 2, 5, and 83.
Prime factorization of 830: 2 × 5 × 83.
The sum of factors of 830: 1 + 2 + 5 + 10 + 83 + 166 + 415 + 830 = 1512
How to Find Factors of 830?
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 830. Identifying the numbers that are multiplied to get the number 830 is the multiplication method.
Step 1: Multiply 830 by 1, 830 × 1 = 830.
Step 2: Check for other numbers that give 830 after multiplying
2 × 415 = 830
5 × 166 = 830
10 × 83 = 830
Therefore, the positive factor pairs of 830 are: (1, 830), (2, 415), (5, 166), and (10, 83). All these factor pairs result in 830. 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 830 by 1, 830 ÷ 1 = 830.
Step 2: Continue dividing 830 by the numbers until the remainder becomes 0.
830 ÷ 1 = 830
830 ÷ 2 = 415
830 ÷ 5 = 166
830 ÷ 10 = 83
Therefore, the factors of 830 are: 1, 2, 5, 10, 83, 166, 415, and 830.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 830 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
830 ÷ 2 = 415
415 ÷ 5 = 83
83 ÷ 83 = 1
The prime factors of 830 are 2, 5, and 83. The prime factorization of 830 is: 2 × 5 × 83.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 830 is divided by 2 to get 415.
Step 2: Now divide 415 by 5 to get 83. Step 3: Divide 83 by 83 to get 1. So, the prime factorization of 830 is: 2 × 5 × 83.
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 830: (1, 830), (2, 415), (5, 166), and (10, 83).
- Negative factor pairs of 830: (-1, -830), (-2, -415), (-5, -166), and (-10, -83).
Common Mistakes and How to Avoid Them in Factors of 830
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 830, 1 and 830 are also factors.
Factors of 830 Examples
Problem 1
There are 10 teachers and 830 students. How will they divide students equally among teachers?
They will get 83 students each.
Explanation
To divide the students equally, we need to divide the total students with the number of teachers.
830/10 = 83
Problem 2
A rectangular stage has a length of 5 meters and a total area of 830 square meters. Find the width?
166 meters.
Explanation
To find the width of the stage, we use the formula,
Area = length × width
830 = 5 × width
To find the value of width, we need to shift 5 to the left side.
830/5 = width
Width = 166.
Problem 3
There are 415 chairs and 2 sections in an auditorium. How many chairs will be in each section?
Each section will have 207 chairs.
Explanation
To find the chairs in each section, divide the total chairs by the sections. 415/2 = 207.5 (round to nearest whole number for practical purposes if needed)
Problem 4
In a company, there are 830 employees, and 83 departments. How many employees are there in each department?
There are 10 employees in each department.
Explanation
Dividing the employees with the total departments, we will get the number of employees in each department.
830/83 = 10
Problem 5
830 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 166 books.
Explanation
Divide total books by shelves.
830/5 = 166
FAQs on Factors of 830
1.What are the factors of 830?
2.Mention the prime factors of 830.
3.Is 830 a multiple of 5?
4.Mention the factor pairs of 830?
5.What is the square of 830?
6.How can children in United States use numbers in everyday life to understand Factors of 830?
7.What are some fun ways kids in United States can practice Factors of 830 with numbers?
8.What role do numbers and Factors of 830 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 830 skills?
Important Glossaries for Factor of 830
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 830 are 1, 2, 5, 10, 83, 166, 415, and 830.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 83 are prime factors of 830.
- 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 830 are (1, 830), (2, 415), (5, 166), and (10, 83).
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 830 is 2 × 5 × 83.
- Multiple: A number that can be divided by another number without a remainder. For example, 830 is a multiple of 5.
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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.
