Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
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.
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.
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 10 teachers and 830 students. How will they divide students equally among teachers?
They will get 83 students each.
To divide the students equally, we need to divide the total students with the number of teachers.
830/10 = 83
A rectangular stage has a length of 5 meters and a total area of 830 square meters. Find the width?
166 meters.
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.
There are 415 chairs and 2 sections in an auditorium. How many chairs will be in each section?
Each section will have 207 chairs.
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)
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.
Dividing the employees with the total departments, we will get the number of employees in each department.
830/83 = 10
830 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 166 books.
Divide total books by shelves.
830/5 = 166
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.
: She loves to read number jokes and games.