129 LearnersLast updated on May 26th, 2025
Factors of 2015
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 2015, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2015?
The numbers that divide 2015 evenly are known as factors of 2015.
A factor of 2015 is a number that divides the number without remainder.
The factors of 2015 are 1, 5, 13, 31, 65, 155, 403, and 2015.
Negative factors of 2015: -1, -5, -13, -31, -65, -155, -403, and -2015.
Prime factors of 2015: 5, 13, and 31.
Prime factorization of 2015: 5 × 13 × 31.
The sum of factors of 2015: 1 + 5 + 13 + 31 + 65 + 155 + 403 + 2015 = 2688
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How to Find Factors of 2015?
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 2015. Identifying the numbers which are multiplied to get the number 2015 is the multiplication method.
Step 1: Multiply 2015 by 1, 2015 × 1 = 2015.
Step 2: Check for other numbers that give 2015 after multiplying.
5 × 403 = 2015
13 × 155 = 2015
31 × 65 = 2015
Therefore, the positive factor pairs of 2015 are: (1, 2015), (5, 403), (13, 155), (31, 65).
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 2015 by 1, 2015 ÷ 1 = 2015.
Step 2: Continue dividing 2015 by the numbers until the remainder becomes 0.
2015 ÷ 1 = 2015
2015 ÷ 5 = 403
2015 ÷ 13 = 155
2015 ÷ 31 = 65
Therefore, the factors of 2015 are: 1, 5, 13, 31, 65, 155, 403, 2015.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 2015 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2015 ÷ 5 = 403
403 ÷ 13 = 31
31 ÷ 31 = 1
The prime factors of 2015 are 5, 13, and 31.
The prime factorization of 2015 is: 5 × 13 × 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, 2015 is divided by 5 to get 403.
Step 2: Now divide 403 by 13 to get 31.
Step 3: 31 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 2015 is: 5 × 13 × 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 2015: (1, 2015), (5, 403), (13, 155), and (31, 65).
Negative factor pairs of 2015: (-1, -2015), (-5, -403), (-13, -155), and (-31, -65).
Common Mistakes and How to Avoid Them in Factors of 2015
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 2015, 1 and 2015 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 2015 consist of -1, -5, -13, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 2.5 as a factor, because 2015/2.5 = 806, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 2015 are prime numbers.
For example, 5, 13, and 31 are the prime factors of 2015, but it has other factors like 65, 155.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 2015 as 5 × 13 × 31 and missing all the key factors.
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Factors of 2015 Examples
Problem 1
There are 5 teams and 2015 points. How will they divide it equally?
They will get 403 points each.
Explanation
To divide the points equally, we need to divide the total points with the number of teams.
2015/5 = 403
Problem 2
A poster is rectangular, the height of the poster is 13 meters and the total area is 2015 square meters. Find the width?
155 meters.
Explanation
To find the width of the poster, we use the formula,
Area = height × width
2015 = 13 × width
To find the value of width, we need to shift 13 to the left side.
2015/13 = width
Width = 155.
Problem 3
There are 31 containers and 2015 kilograms of rice. How many kilograms will be in each container?
Each container will have 65 kilograms.
Explanation
To find the rice in each container, divide the total kilograms with the containers.
2015/31 = 65
Problem 4
In a class, there are 155 students, and 13 groups. How many students are there in each group?
There are 12 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
155/13 = 12
Problem 5
2015 books need to be arranged in 31 shelves. How many books will go on each shelf?
Each of the shelves has 65 books.
Explanation
Divide total books with shelves.
2015/31 = 65
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FAQs on Factors of 2015
1.What are the factors of 2015?
2.Mention the prime factors of 2015.
3.Is 2015 a multiple of 5?
4.Mention the factor pairs of 2015?
5.What is the square of 2015?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 2015?
7.What are some fun ways kids in Vietnam can practice Factors of 2015 with numbers?
8.What role do numbers and Factors of 2015 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 2015 skills?
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Important Glossaries for Factor of 2015
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2015 are 1, 5, 13, 31, 65, 155, 403, and 2015.
- Prime factors: The factors which are prime numbers. For example, 5, 13, and 31 are prime factors of 2015.
- 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 2015 are (1, 2015), (5, 403), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 2015 is 5 × 13 × 31.
- Multiple: A number that can be divided by another number without a remainder. For example, 2015 is a multiple of 5.
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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.
