101 LearnersLast updated on May 26th, 2025
Factors of 856
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 856, how they are used in real life, and tips to learn them quickly.
What are the Factors of 856?
The numbers that divide 856 evenly are known as factors of 856.
A factor of 856 is a number that divides the number without a remainder.
The factors of 856 are 1, 2, 4, 8, 107, 214, 428, and 856.
Negative factors of 856: -1, -2, -4, -8, -107, -214, -428, and -856.
Prime factors of 856: 2 and 107.
Prime factorization of 856: 2³ × 107.
The sum of factors of 856: 1 + 2 + 4 + 8 + 107 + 214 + 428 + 856 = 1620
How to Find Factors of 856?
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 856. Identifying the numbers which are multiplied to get the number 856 is the multiplication method.
Step 1: Multiply 856 by 1, 856 × 1 = 856.
Step 2: Check for other numbers that give 856 after multiplying:
2 × 428 = 856
4 × 214 = 856
8 × 107 = 856
Therefore, the positive factor pairs of 856 are: (1, 856), (2, 428), (4, 214), (8, 107).
All these factor pairs result in 856.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Divide the given number by whole numbers until the remainder becomes zero and list out the numbers that result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 856 by 1, 856 ÷ 1 = 856.
Step 2: Continue dividing 856 by the numbers until the remainder becomes 0.
856 ÷ 1 = 856
856 ÷ 2 = 428
856 ÷ 4 = 214
856 ÷ 8 = 107
Therefore, the factors of 856 are: 1, 2, 4, 8, 107, 214, 428, 856.
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 856 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
856 ÷ 2 = 428
428 ÷ 2 = 214
214 ÷ 2 = 107
107 ÷ 107 = 1
The prime factors of 856 are 2 and 107.
The prime factorization of 856 is: 2³ × 107.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 856 is divided by 2 to get 428.
Step 2: Now divide 428 by 2 to get 214.
Step 3: Then divide 214 by 2 to get 107. Here, 107 is a prime number and cannot be divided anymore. So, the prime factorization of 856 is: 2³ × 107.
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 856: (1, 856), (2, 428), (4, 214), (8, 107).
Negative factor pairs of 856: (-1, -856), (-2, -428), (-4, -214), (-8, -107).
Common Mistakes and How to Avoid Them in Factors of 856
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 856, 1 and 856 are also factors.
Factors of 856 Examples
Problem 1
There are 8 buses and 856 passengers. How will they distribute equally?
They will get 107 passengers each.
Explanation
To distribute the passengers equally, we need to divide the total passengers by the number of buses.
856/8 = 107
Problem 2
A rectangular garden has a length of 4 meters and a total area of 856 square meters. Find the width?
214 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
856 = 4 × width
To find the value of the width, we need to divide by 4.
856/4 = width
Width = 214.
Problem 3
There are 856 candies and 4 bags. How many candies will be in each bag?
Each bag will have 214 candies.
Explanation
To find the candies in each bag, divide the total candies by the number of bags.
856/4 = 214
Problem 4
In a school, there are 856 students, and 8 classes. How many students are there in each class?
There are 107 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
856/8 = 107
Problem 5
856 books need to be arranged on 8 shelves. How many books will go on each shelf?
Each of the shelves has 107 books.
Explanation
Divide total books by shelves.
856/8 = 107
FAQs on Factors of 856
1.What are the factors of 856?
2.Mention the prime factors of 856.
3.Is 856 a multiple of 4?
4.Mention the factor pairs of 856?
5.What is the square of 856?
Important Glossaries for Factor of 856
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 856 are 1, 2, 4, 8, 107, 214, 428, 856.
- Prime factors: The factors which are prime numbers. For example, 2 and 107 are prime factors of 856.
- 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 856 are (1, 856), (2, 428), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, 856 can be expressed as 2³ × 107.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to the given number. For example, using multiplication, we find that 4 × 214 = 856.
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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.
