101 LearnersLast updated on May 26th, 2025
Factors of 861
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 861, how they are used in real life, and tips to learn them quickly.
What are the Factors of 861?
The numbers that divide 861 evenly are known as factors of 861.
A factor of 861 is a number that divides the number without remainder.
The factors of 861 are 1, 3, 9, 27, 31, 93, 279, and 861.
Negative factors of 861: -1, -3, -9, -27, -31, -93, -279, and -861.
Prime factors of 861: 3 and 31.
Prime factorization of 861: 33 × 31.
The sum of factors of 861: 1 + 3 + 9 + 27 + 31 + 93 + 279 + 861 = 1304
How to Find Factors of 861?
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 861. Identifying the numbers which are multiplied to get the number 861 is the multiplication method.
Step 1: Multiply 861 by 1, 861 × 1 = 861.
Step 2: Check for other numbers that give 861 after multiplying
3 × 287 = 861
9 × 95 = 861
27 × 31 = 861
Therefore, the positive factor pairs of 861 are: (1, 861), (3, 287), (9, 95), and (27, 31).
All these factor pairs result in 861.
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 861 by 1, 861 ÷ 1 = 861.
Step 2: Continue dividing 861 by the numbers until the remainder becomes 0.
861 ÷ 1 = 861
861 ÷ 3 = 287
861 ÷ 9 = 95
861 ÷ 27 = 31
Therefore, the factors of 861 are: 1, 3, 9, 27, 31, 93, 279, 861.
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 861 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
861 ÷ 3 = 287
287 ÷ 3 = 95
95 ÷ 3 = 31
The prime factors of 861 are 3 and 31.
The prime factorization of 861 is: 33 × 31.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 861 is divided by 3 to get 287.
Step 2: Now divide 287 by 3 to get 95. Step 3: Then divide 95 by 3 to get 31. Here, 31 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 861 is: 33 × 31.
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 861: (1, 861), (3, 287), (9, 95), and (27, 31).
Negative factor pairs of 861: (-1, -861), (-3, -287), (-9, -95), and (-27, -31).
Common Mistakes and How to Avoid Them in Factors of 861
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 word. Always remember to include 1 and the number itself.
For example, in factors of 861, 1 and 861 are also factors.
Factors of 861 Examples
Problem 1
There are 9 teams and 861 players. How will they distribute the players equally?
They will have 95 players in each team.
Explanation
To divide the players equally, we need to divide the total number of players by the number of teams.
861/9 = 95
Problem 2
A rectangular garden has a length of 31 meters and a total area of 861 square meters. Find the width?
27 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
861 = 31 × width
To find the value of width, we need to shift 31 to the left side.
861/31 = width
Width = 27.
Problem 3
There are 3 buses and 861 passengers. How many passengers will be in each bus?
Each bus will have 287 passengers.
Explanation
To find the passengers in each bus, divide the total passengers by the number of buses.
861/3 = 287
Problem 4
In a class, there are 861 students, and 31 groups. How many students are there in each group?
There are 27 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
861/31 = 27
Problem 5
861 books need to be arranged in 9 shelves. How many books will go on each shelf?
Each of the shelves has 95 books.
Explanation
Divide total books by shelves.
861/9 = 95
FAQs on Factors of 861
1.What are the factors of 861?
2.Mention the prime factors of 861.
3.Is 861 a multiple of 9?
4.Mention the factor pairs of 861?
5.What is the square of 861?
Important Glossaries for Factor of 861
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 861 are 1, 3, 9, 27, 31, 93, 279, and 861.
- Prime factors: The factors which are prime numbers. For example, 3 and 31 are prime factors of 861.
- 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 861 are (1, 861), (3, 287), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 861 is 33 × 31.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 861 is a multiple of 9.
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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.
