100 LearnersLast updated on May 26th, 2025
Factors of 857
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 857, how they are used in real life, and tips to learn them quickly.
What are the Factors of 857?
The numbers that divide 857 evenly are known as factors of 857.
A factor of 857 is a number that divides the number without a remainder.
The factors of 857 are 1, 7, 11, 77, 13, 91, 119, and 857.
Negative factors of 857: -1, -7, -11, -77, -13, -91, -119, and -857.
Prime factors of 857: 7, 11, and 13.
Prime factorization of 857: (7 times 11 times 13).
The sum of factors of 857: 1 + 7 + 11 + 77 + 13 + 91 + 119 + 857 = 1176
How to Find Factors of 857?
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 857. Identifying the numbers which are multiplied to get the number 857 is the multiplication method.
Step 1: Multiply 857 by 1, (857 times 1 = 857).
Step 2: Check for other numbers that give 857 after multiplying \(7 \times 11 \times 13 = 857\)
Therefore, the positive factor pairs of 857 are: (1, 857), (7, 11, 13).
All these factor pairs result in 857.
For every positive factor, there is a negative factor.
Finding Factors Using 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 simple division method
Step 1: Divide 857 by 1, \(857 \div 1 = 857\).
Step 2: Continue dividing 857 by the numbers until the remainder becomes 0.
(857 div 1 = 857)
(857 div 7 = 122.428)
(857 div 11 = 77.909)
(857 div 13 = 65.923)
Therefore, the factors of 857 are: 1 and 857.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 857 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
(857 div 7 = 122.428)
(857 div 11 = 77.909)
(857 div 13 = 65.923)
The prime factors of 857 are 7, 11, and 13.
The prime factorization of 857 is: (7 times 11 times 13).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 857 can be expressed as (7 times 11 times 13). Here, these are the smallest prime numbers that cannot be divided anymore. So, the prime factorization of 857 is: (7 times 11 times 13).
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 857: (1, 857).
Negative factor pairs of 857: (-1, -857).
Common Mistakes and How to Avoid Them in Factors of 857
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 857, 1 and 857 are also factors.
Factors of 857 Examples
Problem 1
There are 13 people and 857 apples. How will they divide it equally?
They will get 65 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of people.
(857/13 = 65)
Problem 2
A rectangular garden has a length of 11 meters and a total area of 857 square meters. Find the width?
77 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
(857 = 11 times) width
To find the value of width, we need to shift 11 to the left side.
(857/11 =) width
Width = 77.
Problem 3
There are 7 groups and 857 marbles. How many marbles will be in each group?
Each group will have 122 marbles, with 3 marbles remaining.
Explanation
To find the marbles in each group, divide the total marbles with the groups.
(857/7 = 122) R3
Problem 4
In a class, there are 119 students, and 7 teams. How many students are there in each team?
There are 17 students in each team.
Explanation
Dividing the students with the total teams, we will get the number of students in each team.
(119/7 = 17)
Problem 5
857 books need to be arranged in 11 shelves. How many books will go on each shelf?
Each of the shelves has 77 books, with 10 books remaining.
Explanation
Divide total books with shelves. (857/11 = 77) R10
FAQs on Factors of 857
1.What are the factors of 857?
2.Mention the prime factors of 857.
3.Is 857 a multiple of 13?
4.Mention the factor pairs of 857?
5.What is the square of 857?
Important Glossaries for Factors of 857
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 857 are 1, 7, 11, 77, 13, 91, 119, and 857.
- Prime factors: The factors which are prime numbers. For example, 7, 11, and 13 are prime factors of 857.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pair of 857 is (1, 857).
- Prime factorization: Breaking down a number into the multiplication of its prime factors. For example, the prime factorization of 857 is (7 times 11 times 13).
- Multiplication method: Identifying pairs of numbers that multiply to give the original number. For example, using the multiplication method to find that (7 times 11 times 13 = 857).
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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.
