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192 LearnersLast updated on December 16, 2025
Factors of 520
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.
What are the Factors of 520?
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
| Factor Type | Values |
| Positive Factors of 520 | (1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520) |
| Negative Factors of 520 | (-1, -2, -4, -5, -8, -10, -13, -20, -26, -40, -52, -65, -104, -130, -260, -520) |
| Prime Factors of 520 | (2, 5, 13) |
| Prime Factorization of 520 | 23 × 5 × 13 |
| Sum of factors of 520 | 1260 |
How to Find Factors of 520?
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 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.
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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 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.
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 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.
Prime factors of 520
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.
Prime Factorization of 520
Prime Factorization breaks down the prime factors of 520.
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 of 75
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:
| Factors | Positive Pair Factors |
| 1 × 520 = 520 | 1, 520 |
| 2 × 260 = 520 | 2, 260 |
| 4 × 130 = 520 | 4, 130 |
| 5 × 104 = 520 | 5, 104 |
| 8 × 65 = 520 | 8, 65 |
| 10 × 52 = 520 | 10, 52 |
| 13 × 40 = 520 | 13, 40 |
| 20 × 26 = 520 | 20, 26 |
Negative factor pairs of 520:
| Factors | Negative Pair Factors |
| −1 × −520 = 520 | −1, −520 |
| −2 × −260 = 520 | −2, −260 |
| −4 × −130 = 520 | −4, −130 |
| −5 × −104 = 520 | −5, −104 |
| −8 × −65 = 520 | −8, −65 |
| −10 × −52 = 520 | −10, −52 |
| −13 × −40 = 520 | −13, −40 |
| −20 × −26 = 520 | −20, −26 |
Common Mistakes and How to Avoid Them in Factors of 520
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 520, 1 and 520 are also factors.
Mistake 2
Missing Negative Factors
We tend to mention only positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 520 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 520/1.5 = 346.666, 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 520 are prime numbers.
For example, 2, 5, and 13 are the prime factors of 520, but it has other factors like 4, 10, and so on.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 520 as 23 × 5 × 13 and missing all the key factors.
Factors of 520 Examples
Problem 1
There are 13 friends and 520 candies. How will they divide it equally?
They will get 40 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
520/13 = 40
Problem 2
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.
Explanation
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.
FAQs on Factors of 520
1.What are the factors of 520?
2.Mention the prime factors of 520.
3.Is 520, a multiple of 4?
4.Mention the factor pairs of 520?
5.What is the square of 520?
6.How many factors does 520 have?
7.What is the smallest factor of 520?
8.What is the largest factor of 520?
9.Which factors of 520 add up to 13?
10.How many even factors does 520 have?
11.What are the odd factors of 520?
12.What is the sum of all the factors of 520?
Important Glossaries for Factors of 520
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, and 520.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 13 are prime factors of 520.
- 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 520 are (1, 520), (2, 260), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For 520, it is 2^3 × 5 × 13.
- Division method: A method of finding factors by dividing the number by integers to see which ones result in a remainder of zero.
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.
