Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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: 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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 5 teams and 2015 points. How will they divide it equally?
They will get 403 points each.
To divide the points equally, we need to divide the total points with the number of teams.
2015/5 = 403
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.
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.
There are 31 containers and 2015 kilograms of rice. How many kilograms will be in each container?
Each container will have 65 kilograms.
To find the rice in each container, divide the total kilograms with the containers.
2015/31 = 65
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.
Dividing the students with the total groups, we will get the number of students in each group.
155/13 = 12
2015 books need to be arranged in 31 shelves. How many books will go on each shelf?
Each of the shelves has 65 books.
Divide total books with shelves.
2015/31 = 65
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.
: She loves to read number jokes and games.