Factors of 513
2026-02-28 17:23 Diff
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Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 513, how they are used in real life, and the tips to learn them quickly.

What are the Factors of 513?

The numbers that divide 513 evenly are known as factors of 513.

A factor of 513 is a number that divides the number without remainder.

The factors of 513 are 1, 3, 171, and 513.

Negative factors of 513: -1, -3, -171, and -513.

Prime factors of 513: 3 and 171.

Prime factorization of 513: 3 × 171.

The sum of factors of 513: 1 + 3 + 171 + 513 = 688

How to Find Factors of 513?

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 513. Identifying the numbers which are multiplied to get the number 513 is the multiplication method.

Step 1: Multiply 513 by 1, 513 × 1 = 513.

Step 2: Check for other numbers that give 513 after multiplying 3 × 171 = 513

Therefore, the positive factor pairs of 513 are: (1, 513) and (3, 171). All these factor pairs result in 513.

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 513 by 1, 513 ÷ 1 = 513.

Step 2: Continue dividing 513 by the numbers until the remainder becomes 0.

513 ÷ 1 = 513

513 ÷ 3 = 171

513 ÷ 171 = 3

Therefore, the factors of 513 are: 1, 3, 171, and 513.

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: In this process, prime factors of 513 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

513 ÷ 3 = 171

171 ÷ 3 = 57

57 ÷ 3 = 19

19 is a prime number and cannot be divided further. The prime factors of 513 are 3 and 19.

The prime factorization of 513 is: 3 × 3 × 3 × 19.

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows

Step 1: Firstly, 513 is divided by 3 to get 171.

Step 2: Now divide 171 by 3 to get 57.

Step 3: Then divide 57 by 3 to get 19, which is a prime number. Here, 19 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 513 is: 3 × 3 × 3 × 19.

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 513: (1, 513) and (3, 171).

Negative factor pairs of 513: (-1, -513) and (-3, -171).

Common Mistakes and How to Avoid Them in Factors of 513

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

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Problem 1

There are 9 friends and 513 candies. How will they divide it equally?

Okay, lets begin

They will get 57 candies each.

Explanation

To divide the candies equally, we need to divide the total candies by the number of friends.

513/9 = 57

Well explained 👍

Problem 2

A field is rectangular, the length of the field is 3 meters, and the total area is 513 square meters. Find the width.

Okay, lets begin

171 meters.

Explanation

To find the width of the field, we use the formula, Area = length × width

513 = 3 × width

To find the value of width, we need to shift 3 to the left side.

513/3 = width

Width = 171.

Well explained 👍

Problem 3

There are 57 bags and 513 candies. How many candies will be in each bag?

Okay, lets begin

Each bag will have 9 candies.

Explanation

To find the candies in each bag, divide the total candies by the number of bags.

513/57 = 9

Well explained 👍

Problem 4

In a class, there are 513 students, and 3 groups. How many students are there in each group?

Okay, lets begin

There are 171 students in each group.

Explanation

Dividing the students by the total groups, we will get the number of students in each group.

513/3 = 171

Well explained 👍

Problem 5

513 books need to be arranged in 3 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 171 books.

Explanation

Divide total books by shelves.

513/3 = 171

Well explained 👍

FAQs on Factors of 513

1.What are the factors of 513?

1, 3, 171, and 513 are the factors of 513.

2.Mention the prime factors of 513.

The prime factors of 513 are 3 and 19.

3.Is 513 a multiple of 3?

4.Mention the factor pairs of 513.

(1, 513) and (3, 171) are the factor pairs of 513.

5.What is the square of 513?

Important Glossaries for Factor of 513

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 513 are 1, 3, 171, and 513.
  • Prime factors: The factors which are prime numbers. For example, 3 and 19 are prime factors of 513.
  • 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 513 are (1, 513) and (3, 171).
  • Prime factorization: Expressing a number as a product of prime numbers. For example, 3 × 3 × 3 × 19 is the prime factorization of 513.
  • Multiples: Numbers that can be divided by another number without leaving a remainder. For example, 513 is a multiple of 3.

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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

: She loves to read number jokes and games.