102 LearnersLast updated on May 26th, 2025
Factors of 310
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 310, how they are used in real life, and tips to learn them quickly.
What are the Factors of 310?
The numbers that divide 310 evenly are known as factors of 310.
A factor of 310 is a number that divides the number without a remainder.
The factors of 310 are 1, 2, 5, 10, 31, 62, 155, and 310.
Negative factors of 310: -1, -2, -5, -10, -31, -62, -155, and -310.
Prime factors of 310: 2, 5, and 31.
Prime factorization of 310: 2 × 5 × 31.
The sum of factors of 310: 1 + 2 + 5 + 10 + 31 + 62 + 155 + 310 = 576
How to Find Factors of 310?
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 310. Identifying the numbers which are multiplied to get the number 310 is the multiplication method.
Step 1: Multiply 310 by 1, 310 × 1 = 310.
Step 2: Check for other numbers that give 310 after multiplying
2 × 155 = 310
5 × 62 = 310
10 × 31 = 310
Therefore, the positive factor pairs of 310 are: (1, 310), (2, 155), (5, 62), and (10, 31).
All these factor pairs result in 310.
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 a whole number as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 310 by 1, 310 ÷ 1 = 310.
Step 2: Continue dividing 310 by the numbers until the remainder becomes 0.
310 ÷ 1 = 310
310 ÷ 2 = 155
310 ÷ 5 = 62
310 ÷ 10 = 31
Therefore, the factors of 310 are: 1, 2, 5, 10, 31, 62, 155, 310.
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 310 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
310 ÷ 2 = 155
155 ÷ 5 = 31
31 ÷ 31 = 1
The prime factors of 310 are 2, 5, and 31.
The prime factorization of 310 is: 2 × 5 × 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, 310 is divided by 2 to get 155.
Step 2: Now divide 155 by 5 to get 31.
Step 3: Here, 31 is a prime number and cannot be divided anymore. So, the prime factorization of 310 is: 2 × 5 × 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 310: (1, 310), (2, 155), (5, 62), and (10, 31).
Negative factor pairs of 310: (-1, -310), (-2, -155), (-5, -62), and (-10, -31).
Common Mistakes and How to Avoid Them in Factors of 310
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 310, 1 and 310 are also factors.
Factors of 310 Examples
Problem 1
There are 10 workers and 310 boxes. How will they distribute the boxes equally?
They will get 31 boxes each.
Explanation
To divide the boxes equally, we need to divide the total boxes by the number of workers.
310/10 = 31
Problem 2
A rectangular garden has a length of 62 meters and a total area of 310 square meters. Find the width?
5 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
310 = 62 × width
To find the value of width, we need to shift 62 to the left side.
310/62 = width
Width = 5.
Problem 3
There are 31 jars and 310 candies. How many candies will be in each jar?
Each jar will have 10 candies.
Explanation
To find the candies in each jar, divide the total candies by the jars.
310/31 = 10
Problem 4
In a class, there are 310 students, and 62 groups. How many students are there in each group?
There are 5 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
310/62 = 5
Problem 5
310 books need to be arranged in 2 shelves. How many books will go on each shelf?
Each of the shelves has 155 books.
Explanation
Divide total books with shelves.
310/2 = 155
FAQs on Factors of 310
1.What are the factors of 310?
2.Mention the prime factors of 310.
3.Is 310 a multiple of 5?
4.Mention the factor pairs of 310?
5.What is the square of 310?
6.How can children in Indonesia use numbers in everyday life to understand Factors of 310?
7.What are some fun ways kids in Indonesia can practice Factors of 310 with numbers?
8.What role do numbers and Factors of 310 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Factors of 310 skills?
Important Glossaries for Factor of 310
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 310 are 1, 2, 5, 10, 31, 62, 155, and 310.
- Prime Factors: The factors which are prime numbers. For example, 2, 5, and 31 are prime factors of 310.
- 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 310 are (1, 310), (2, 155), etc.
- Prime Factorization: The process of breaking down a number into its prime numbers. For example, the prime factorization of 310 is 2 × 5 × 31.
- Multiplication Method: A technique to find factors by identifying pairs of numbers that multiply to give a target number, like 310.
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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
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