105 LearnersLast updated on May 26th, 2025
Factors of 834
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 834, how they are used in real life, and tips to learn them quickly.
What are the Factors of 834?
The numbers that divide 834 evenly are known as factors of 834.
A factor of 834 is a number that divides the number without a remainder.
The factors of 834 are 1, 2, 3, 6, 139, 278, 417, and 834.
Negative factors of 834: -1, -2, -3, -6, -139, -278, -417, and -834.
Prime factors of 834: 2, 3, and 139.
Prime factorization of 834: 2 × 3 × 139.
The sum of factors of 834: 1 + 2 + 3 + 6 + 139 + 278 + 417 + 834 = 1680
How to Find Factors of 834?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 834. Identifying the numbers which are multiplied to get the number 834 is the multiplication method.
Step 1: Multiply 834 by 1, 834 × 1 = 834.
Step 2: Check for other numbers that give 834 after multiplying
2 × 417 = 834
3 × 278 = 834
6 × 139 = 834
Therefore, the positive factor pairs of 834 are: (1, 834), (2, 417), (3, 278), (6, 139).
All these factor pairs result in 834.
For every positive factor, there is a negative factor.
Finding Factors Using the Division Method
Dividing the given numbers with 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 834 by 1, 834 ÷ 1 = 834.
Step 2: Continue dividing 834 by the numbers until the remainder becomes 0.
834 ÷ 1 = 834
834 ÷ 2 = 417
834 ÷ 3 = 278
834 ÷ 6 = 139
Therefore, the factors of 834 are: 1, 2, 3, 6, 139, 278, 417, 834.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 834 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
834 ÷ 2 = 417
417 ÷ 3 = 139
139 ÷ 139 = 1
The prime factors of 834 are 2, 3, and 139.
The prime factorization of 834 is: 2 × 3 × 139.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 834 is divided by 2 to get 417.
Step 2: Now divide 417 by 3 to get 139.
Step 3: 139 is a prime number and cannot be divided further. So, the prime factorization of 834 is: 2 × 3 × 139.
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 834: (1, 834), (2, 417), (3, 278), (6, 139).
- Negative factor pairs of 834: (-1, -834), (-2, -417), (-3, -278), (-6, -139).
Common Mistakes and How to Avoid Them in Factors of 834
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 834, 1 and 834 are also factors.
Factors of 834 Examples
Problem 1
There are 6 classrooms and 834 students. How will they divide the students equally among the classrooms?
Each classroom will have 139 students.
Explanation
To divide the students equally, we need to divide the total students by the number of classrooms.
834/6 = 139
Problem 2
A garden is rectangular, the width of the garden is 3 meters and the total area is 834 square meters. Find the length?
278 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
834 = 3 × length
To find the value of the length, we need to shift 3 to the left side.
834/3 = length
Length = 278.
Problem 3
There are 278 seats in a theater and 834 tickets sold. How many people can be seated in each seat?
Each seat will have 3 people.
Explanation
To find the people in each seat, divide the total tickets by the seats.
834/278 = 3
Problem 4
In a school, there are 834 students, and 2 houses. How many students are there in each house?
There are 417 students in each house.
Explanation
Dividing the students by the total houses, we will get the number of students in each house.
834/2 = 417
Problem 5
834 books need to be arranged in 3 sections. How many books will go in each section?
Each section has 278 books.
Explanation
Divide total books by sections.
834/3 = 278
FAQs on Factors of 834
1.What are the factors of 834?
2.Mention the prime factors of 834.
3.Is 834 a multiple of 6?
4.Mention the factor pairs of 834?
5.What is the square of 834?
Important Glossaries for Factors of 834
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 834 are 1, 2, 3, 6, 139, 278, 417, and 834.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 139 are prime factors of 834.
- 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 834 are (1, 834), (2, 417), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the given number.
- Division method: A method to find factors by dividing the number by whole numbers until the remainder is zero.
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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.
