102 LearnersLast updated on May 26th, 2025
Factors of 872
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 872, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 872?
The numbers that divide 872 evenly are known as factors of 872.
A factor of 872 is a number that divides the number without remainder.
The factors of 872 are 1, 2, 4, 8, 109, 218, 436, and 872.
Negative factors of 872: -1, -2, -4, -8, -109, -218, -436, and -872.
Prime factors of 872: 2 and 109.
Prime factorization of 872: 23 × 109.
The sum of factors of 872: 1 + 2 + 4 + 8 + 109 + 218 + 436 + 872 = 1650
How to Find Factors of 872?
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 872. Identifying the numbers which are multiplied to get the number 872 is the multiplication method.
Step 1: Multiply 872 by 1, 872 × 1 = 872.
Step 2: Check for other numbers that give 872 after multiplying
2 × 436 = 872
4 × 218 = 872
8 × 109 = 872
Therefore, the positive factor pairs of 872 are: (1, 872), (2, 436), (4, 218), (8, 109).
All these factor pairs result in 872.
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 in whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide 872 by 1, 872 ÷ 1 = 872.
Step 2: Continue dividing 872 by the numbers until the remainder becomes 0.
872 ÷ 1 = 872
872 ÷ 2 = 436
872 ÷ 4 = 218
872 ÷ 8 = 109
Therefore, the factors of 872 are: 1, 2, 4, 8, 109, 218, 436, 872.
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 872 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
872 ÷ 2 = 436
436 ÷ 2 = 218
218 ÷ 2 = 109
109 ÷ 109 = 1
The prime factors of 872 are 2 and 109.
The prime factorization of 872 is: 23 × 109.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 872 is divided by 2 to get 436.
Step 2: Now divide 436 by 2 to get 218. Step 3: Then divide 218 by 2 to get 109. Here, 109 is the smallest prime number, which cannot be divided anymore. So, the prime factorization of 872 is: 23 × 109.
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 872: (1, 872), (2, 436), (4, 218), (8, 109).
Negative factor pairs of 872: (-1, -872), (-2, -436), (-4, -218), (-8, -109).
Common Mistakes and How to Avoid Them in Factors of 872
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 factors for every word. Always remember to include 1 and the number itself.
For example, in factors of 872, 1 and 872 are also factors.
Factors of 872 Examples
Problem 1
There are 8 friends and 872 marbles. How will they divide it equally?
They will get 109 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles with the number of friends.
872 ÷ 8 = 109
Problem 2
A field is rectangular, the length of the field is 4 meters and the total area is 872 square meters. Find the width.
218 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
872 = 4 × width
To find the value of width, we need to shift 4 to the left side.
872 ÷ 4 = width
Width = 218.
Problem 3
There are 218 bags and 872 apples. How many apples will be in each bag?
Each bag will have 4 apples.
Explanation
To find the apples in each bag, divide the total apples with the bags.
872 ÷ 218 = 4
Problem 4
In a class, there are 872 students, and 109 groups. How many students are there in each group?
There are 8 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
872 ÷ 109 = 8
Problem 5
872 books need to be arranged in 2 shelves. How many books will go on each shelf?
Each of the shelves has 436 books.
Explanation
Divide the total books with shelves.
872 ÷ 2 = 436
FAQs on Factors of 872
1.What are the factors of 872?
2.Mention the prime factors of 872.
3.Is 872 a multiple of 4?
4.Mention the factor pairs of 872.
5.What is the square of 872?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 872?
7.What are some fun ways kids in Vietnam can practice Factors of 872 with numbers?
8.What role do numbers and Factors of 872 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 872 skills?
Important Glossaries for Factor of 872
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 872 are 1, 2, 4, 8, 109, 218, 436, and 872.
- Prime factors: The factors which are prime numbers. For example, 2 and 109 are prime factors of 872.
- 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 872 are (1, 872), (2, 436), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 872 is 23 × 109.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 872 is a multiple of 4.
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About BrightChamps in Vietnam
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.
