100 LearnersLast updated on May 26th, 2025
Factors of 852
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 852, how they are used in real life, and tips to learn them quickly.
What are the Factors of 852?
The numbers that divide 852 evenly are known as factors of 852.
A factor of 852 is a number that divides the number without remainder.
The factors of 852 are 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, and 852.
Negative factors of 852: -1, -2, -3, -4, -6, -12, -71, -142, -213, -284, -426, and -852.
Prime factors of 852: 2, 3, and 71.
Prime factorization of 852: 22 × 3 × 71.
The sum of factors of 852: 1 + 2 + 3 + 4 + 6 + 12 + 71 + 142 + 213 + 284 + 426 + 852 = 2016
How to Find Factors of 852?
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 852. Identifying the numbers which are multiplied to get the number 852 is the multiplication method.
Step 1: Multiply 852 by 1, 852 × 1 = 852.
Step 2: Check for other numbers that give 852 after multiplying
2 × 426 = 852
3 × 284 = 852
4 × 213 = 852
6 × 142 = 852
12 × 71 = 852
Therefore, the positive factor pairs of 852 are: (1, 852), (2, 426), (3, 284), (4, 213), (6, 142), (12, 71).
All these factor pairs result in 852.
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 852 by 1, 852 ÷ 1 = 852.
Step 2: Continue dividing 852 by the numbers until the remainder becomes 0.
852 ÷ 1 = 852
852 ÷ 2 = 426
852 ÷ 3 = 284
852 ÷ 4 = 213
852 ÷ 6 = 142
852 ÷ 12 = 71
Therefore, the factors of 852 are: 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 852 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
852 ÷ 2 = 426
426 ÷ 2 = 213
213 ÷ 3 = 71
71 ÷ 71 = 1
The prime factors of 852 are 2, 3, and 71.
The prime factorization of 852 is: 22 × 3 × 71.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 852 is divided by 2 to get 426.
Step 2: Now divide 426 by 2 to get 213.
Step 3: Then divide 213 by 3 to get 71.
Step 4: Here, 71 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 852 is: 22 × 3 × 71.
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 852: (1, 852), (2, 426), (3, 284), (4, 213), (6, 142), (12, 71).
Negative factor pairs of 852: (-1, -852), (-2, -426), (-3, -284), (-4, -213), (-6, -142), (-12, -71).
Common Mistakes and How to Avoid Them in Factors of 852
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
People 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 852, 1 and 852 are also factors.
Factors of 852 Examples
Problem 1
There are 71 people and 852 candies. How will they divide it equally?
They will get 12 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of people.
852/71 = 12
Problem 2
A rectangular garden has a width of 4 meters and the total area is 852 square meters. Find the length.
213 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
852 = length × 4
To find the value of length, divide both sides by 4.
852/4 = length
Length = 213.
Problem 3
There are 12 crates and 852 apples. How many apples will be in each crate?
Each crate will have 71 apples.
Explanation
To find the apples in each crate, divide the total apples by the number of crates.
852/12 = 71
Problem 4
A library has 852 books and 6 sections. How many books are there in each section?
There are 142 books in each section.
Explanation
Dividing the books by the total sections, we will get the number of books in each section.
852/6 = 142
Problem 5
852 pages need to be distributed among 3 binders. How many pages will go in each binder?
Each binder will hold 284 pages.
Explanation
Divide the total pages by the number of binders.
852/3 = 284
FAQs on Factors of 852
1.What are the factors of 852?
2.Mention the prime factors of 852.
3.Is 852 a multiple of 3?
4.Mention the factor pairs of 852?
5.What is the square of 852?
Important Glossaries for Factor of 852
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 852 are 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 71 are prime factors of 852.
- 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 852 are (1, 852), (2, 426), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 852 is 22 × 3 × 71.
- Multiple: A number that can be divided by another number without a remainder. For example, 852 is a multiple of 3.
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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.
