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 520, how they are used in real life, and tips to learn them quickly.
The numbers that divide 520 evenly are known as factors of 520.
A factor of 520 is a number that divides the number without remainder.
The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, and 520.
Negative factors of 520: -1, -2, -4, -5, -8, -10, -13, -20, -26, -40, -52, -65, -104, -130, -260, and -520.
Prime factors of 520: 2, 5, and 13.
Prime factorization of 520: 23 × 5 × 13.
The sum of factors of 520: 1 + 2 + 4 + 5 + 8 + 10 + 13 + 20 + 26 + 40 + 52 + 65 + 104 + 130 + 260 + 520 = 1260
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 520. Identifying the numbers which are multiplied to get the number 520 is the multiplication method.
Step 1: Multiply 520 by 1, 520 × 1 = 520.
Step 2: Check for other numbers that give 520 after multiplying
2 × 260 = 520
4 × 130 = 520
5 × 104 = 520
8 × 65 = 520
10 × 52 = 520
13 × 40 = 520
20 × 26 = 520
Therefore, the positive factor pairs of 520 are: (1, 520), (2, 260), (4, 130), (5, 104), (8, 65), (10, 52), (13, 40), (20, 26).
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 520 by 1, 520 ÷ 1 = 520.
Step 2: Continue dividing 520 by the numbers until the remainder becomes 0.
520 ÷ 1 = 520
520 ÷ 2 = 260
520 ÷ 4 = 130
520 ÷ 5 = 104
520 ÷ 8 = 65
520 ÷ 10 = 52
520 ÷ 13 = 40
520 ÷ 20 = 26
Therefore, the factors of 520 are: 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 520 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
520 ÷ 2 = 260
260 ÷ 2 = 130
130 ÷ 2 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
The prime factors of 520 are 2, 5, and 13.
The prime factorization of 520 is: 23 × 5 × 13.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 520 is divided by 2 to get 260.
Step 2: Now divide 260 by 2 to get 130.
Step 3: Then divide 130 by 2 to get 65.
Step 4: Divide 65 by 5 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 520 is: 23 × 5 × 13.
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 520: (1, 520), (2, 260), (4, 130), (5, 104), (8, 65), (10, 52), (13, 40), (20, 26).
Negative factor pairs of 520: (-1, -520), (-2, -260), (-4, -130), (-5, -104), (-8, -65), (-10, -52), (-13, -40), (-20, -26).
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 13 friends and 520 candies. How will they divide it equally?
They will get 40 candies each.
To divide the candies equally, we need to divide the total candies by the number of friends.
520/13 = 40
A field is rectangular, the length of the field is 26 meters and the total area is 520 square meters. Find the width?
20 meters.
To find the width of the field, we use the formula,
Area = length × width
520 = 26 × width
To find the value of width, we need to shift 26 to the left side.
520/26 = width
Width = 20.
There are 65 bags and 520 apples. How many apples will be in each bag?
Each bag will have 8 apples.
To find the apples in each bag, divide the total apples by the bags.
520/65 = 8
In a class, there are 520 students, and 10 groups. How many students are there in each group?
There are 52 students in each group.
Dividing the students by the total groups, we will get the number of students in each group.
520/10 = 52
520 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 104 books.
Divide total books by shelves.
520/5 = 104
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.