100 LearnersLast updated on May 26th, 2025
Factors of 2310
Factors are the numbers that divide any given number evenly without a 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 2310, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2310?
The numbers that divide 2310 evenly are known as factors of 2310.
A factor of 2310 is a number that divides the number without a remainder.
The factors of 2310 are 1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, and 2310.
Negative factors of 2310: -1, -2, -3, -5, -6, -7, -10, -11, -14, -15, -21, -22, -30, -33, -35, -42, -55, -66, -70, -77, -105, -110, -154, -165, -210, -231, -330, -385, -462, -770, -1155, and -2310.
Prime factors of 2310: 2, 3, 5, 7, and 11.
Prime factorization of 2310: 2 × 3 × 5 × 7 × 11.
The sum of factors of 2310: 1 + 2 + 3 + 5 + 6 + 7 + 10 + 11 + 14 + 15 + 21 + 22 + 30 + 33 + 35 + 42 + 55 + 66 + 70 + 77 + 105 + 110 + 154 + 165 + 210 + 231 + 330 + 385 + 462 + 770 + 1155 + 2310 = 6552
How to Find Factors of 2310?
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 2310. Identifying the numbers which are multiplied to get the number 2310 is the multiplication method.
Step 1: Multiply 2310 by 1, 2310 × 1 = 2310.
Step 2: Check for other numbers that give 2310 after multiplying:
2 × 1155 = 2310
3 × 770 = 2310
5 × 462 = 2310
6 × 385 = 2310
7 × 330 = 2310
10 × 231 = 2310
11 × 210 = 2310
14 × 165 = 2310
15 × 154 = 2310
21 × 110 = 2310
22 × 105 = 2310
30 × 77 = 2310
33 × 70 = 2310
35 × 66 = 2310
42 × 55 = 2310
Therefore, the positive factor pairs of 2310 are: (1, 2310), (2, 1155), (3, 770), (5, 462), (6, 385), (7, 330), (10, 231), (11, 210), (14, 165), (15, 154), (21, 110), (22, 105), (30, 77), (33, 70), (35, 66), and (42, 55).
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 2310 by 1, 2310 ÷ 1 = 2310.
Step 2: Continue dividing 2310 by the numbers until the remainder becomes 0.
2310 ÷ 1 = 2310
2310 ÷ 2 = 1155
2310 ÷ 3 = 770
2310 ÷ 5 = 462
2310 ÷ 6 = 385
2310 ÷ 7 = 330
2310 ÷ 10 = 231
2310 ÷ 11 = 210
2310 ÷ 14 = 165
2310 ÷ 15 = 154
2310 ÷ 21 = 110
2310 ÷ 22 = 105
2310 ÷ 30 = 77
2310 ÷ 33 = 70
2310 ÷ 35 = 66
2310 ÷ 42 = 55
Therefore, the factors of 2310 are: 1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, and 2310.
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 2310 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2310 ÷ 2 = 1155
1155 ÷ 3 = 385
385 ÷ 5 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1
The prime factors of 2310 are 2, 3, 5, 7, and 11.
The prime factorization of 2310 is: 2 × 3 × 5 × 7 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 2310 is divided by 2 to get 1155.
Step 2: Now divide 1155 by 3 to get 385.
Step 3: Then divide 385 by 5 to get 77.
Step 4: Divide 77 by 7 to get 11.
Here, 11 is a prime number that cannot be divided anymore.
So, the prime factorization of 2310 is: 2 × 3 × 5 × 7 × 11.
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 2310: (1, 2310), (2, 1155), (3, 770), (5, 462), (6, 385), (7, 330), (10, 231), (11, 210), (14, 165), (15, 154), (21, 110), (22, 105), (30, 77), (33, 70), (35, 66), and (42, 55).
Negative factor pairs of 2310: (-1, -2310), (-2, -1155), (-3, -770), (-5, -462), (-6, -385), (-7, -330), (-10, -231), (-11, -210), (-14, -165), (-15, -154), (-21, -110), (-22, -105), (-30, -77), (-33, -70), (-35, -66), and (-42, -55).
Common Mistakes and How to Avoid Them in Factors of 2310
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 2310, 1 and 2310 are also factors.
Factors of 2310 Examples
Problem 1
There are 21 people and 2310 apples. How will they divide it equally?
They will get 110 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of people.
2310/21 = 110
Problem 2
A rectangular garden has a length of 33 meters and a total area of 2310 square meters. Find the width.
70 meters.
Explanation
To find the width of the garden, we use the formula:
Area = length × width
2310 = 33 × width
To find the value of the width, we need to shift 33 to the left side.
2310/33 = width
Width = 70.
Problem 3
There are 42 boxes and 2310 oranges. How many oranges will be in each box?
Each box will have 55 oranges.
Explanation
To find the oranges in each box, divide the total oranges by the number of boxes.
2310/42 = 55
Problem 4
In a class, there are 2310 students, and 10 groups. How many students are there in each group?
There are 231 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
2310/10 = 231
Problem 5
2310 books need to be arranged on 11 shelves. How many books will go on each shelf?
Each of the shelves has 210 books.
Explanation
Divide total books by shelves.
2310/11 = 210
FAQs on Factors of 2310
1.What are the factors of 2310?
2.Mention the prime factors of 2310.
3.Is 2310 a multiple of 7?
4.Mention the factor pairs of 2310?
5.What is the prime factorization of 2310?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 2310?
7.What are some fun ways kids in Vietnam can practice Factors of 2310 with numbers?
8.What role do numbers and Factors of 2310 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 2310 skills?
Important Glossaries for Factors of 2310
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2310 are 1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, and 2310.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, 7, and 11 are prime factors of 2310.
- 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 2310 are (1, 2310), (2, 1155), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 2310 is 2 × 3 × 5 × 7 × 11.
- Multiples: Numbers that can be divided by another number without leaving a remainder. For example, 2310 is a multiple of 7.
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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
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