100 LearnersLast updated on May 26th, 2025
Factors of 870
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 870, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 870?
The numbers that divide 870 evenly are known as factors of 870.
A factor of 870 is a number that divides the number without remainder.
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, and 870.
Negative factors of 870: -1, -2, -3, -5, -6, -10, -15, -29, -30, -58, -87, -145, -174, -290, -435, and -870.
Prime factors of 870: 2, 3, 5, and 29.
Prime factorization of 870: 2 × 3 × 5 × 29.
The sum of factors of 870: 1 + 2 + 3 + 5 + 6 + 10 + 15 + 29 + 30 + 58 + 87 + 145 + 174 + 290 + 435 + 870 = 2160
How to Find Factors of 870?
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 870. Identifying the numbers which are multiplied to get the number 870 is the multiplication method.
Step 1: Multiply 870 by 1, 870 × 1 = 870.
Step 2: Check for other numbers that give 870 after multiplying
2 × 435 = 870
3 × 290 = 870
5 × 174 = 870
6 × 145 = 870
10 × 87 = 870
15 × 58 = 870
29 × 30 = 870
Therefore, the positive factor pairs of 870 are: (1, 870), (2, 435), (3, 290), (5, 174), (6, 145), (10, 87), (15, 58), (29, 30).
All these factor pairs result in 870.
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 870 by 1, 870 ÷ 1 = 870.
Step 2: Continue dividing 870 by the numbers until the remainder becomes 0.
870 ÷ 1 = 870
870 ÷ 2 = 435
870 ÷ 3 = 290
870 ÷ 5 = 174
870 ÷ 6 = 145
870 ÷ 10 = 87
870 ÷ 15 = 58
870 ÷ 29 = 30
Therefore, the factors of 870 are: 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870.
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 870 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
870 ÷ 2 = 435
435 ÷ 3 = 145
145 ÷ 5 = 29
29 ÷ 29 = 1
The prime factors of 870 are 2, 3, 5, and 29.
The prime factorization of 870 is: 2 × 3 × 5 × 29.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 870 is divided by 2 to get 435.
Step 2: Now divide 435 by 3 to get 145.
Step 3: Then divide 145 by 5 to get 29. Here, 29 is a prime number that cannot be divided anymore. So, the prime factorization of 870 is: 2 × 3 × 5 × 29.
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 870: (1, 870), (2, 435), (3, 290), (5, 174), (6, 145), (10, 87), (15, 58), and (29, 30).
Negative factor pairs of 870: (-1, -870), (-2, -435), (-3, -290), (-5, -174), (-6, -145), (-10, -87), (-15, -58), and (-29, -30).
Common Mistakes and How to Avoid Them in Factors of 870
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and 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 870, 1 and 870 is also a factor.
Factors of 870 Examples
Problem 1
There are 15 teachers and 870 students. How will they divide the students equally among themselves?
Each teacher will have 58 students.
Explanation
To divide the students equally, we need to divide the total number of students by the number of teachers.
870/15 = 58
Problem 2
A banner is rectangular, the width of the banner is 29 inches, and the total area is 870 square inches. Find the length.
30 inches.
Explanation
To find the length of the banner, we use the formula, Area = length × width
870 = 29 × length
To find the value of length, divide both sides by 29.
870/29 = length
Length = 30
Problem 3
There are 10 storage boxes and 870 items. How many items will be in each box?
Each box will have 87 items.
Explanation
To find the number of items in each box, divide the total items by the number of boxes.
870/10 = 87
Problem 4
In a conference, there are 870 participants, and 5 groups. How many participants are there in each group?
There are 174 participants in each group.
Explanation
Dividing the participants by the total number of groups, we will get the number of participants in each group.
870/5 = 174
Problem 5
870 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each of the shelves has 145 books.
Explanation
Divide the total books by the number of shelves.
870/6 = 145
FAQs on Factors of 870
1.What are the factors of 870?
2.Mention the prime factors of 870.
3.Is 870 a multiple of 3?
4.Mention the factor pairs of 870?
5.What is the square of 870?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 870?
7.What are some fun ways kids in Vietnam can practice Factors of 870 with numbers?
8.What role do numbers and Factors of 870 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 870 skills?
Important Glossaries for Factors of 870
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, and 870.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 29 are prime factors of 870.
- 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 870 are (1, 870), (2, 435), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 870 is 2 × 3 × 5 × 29.
- Multiples: The result of multiplying a number by an integer. For example, 870 is a multiple of 1, 2, 3, etc.
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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.
