Factors of 519: Prime Factorization, Methods, and Examples

519 is an odd composite number. It has 4 factors. This means the numbers that evenly divide the given number are named as their factors. The factors of 519 are both positive and negative. 

Factors Of 519

The article provides several other details about the factorization process.

Factors of 519

Here are the factors of number 519.

Factors of 519: 1, 3, 173, and 519

Negative Factors of 519

The negative factors of 519 are similar to its positive aspects, just with a negative sign.

Negative Factors of 519: -1, -3, -173, and -519

Prime Factorization of 519

The prime factorization of 519 is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 173

In this article, we will learn about the factors of 519 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 519?

The factors of 519 are 1, 3, 173, and 519. These numbers are the factors as they do not leave any remainder when divided by 519.

The factors of 519 are classified as prime numbers and composite numbers. The prime factors of the number 519 can be determined using the prime factorization technique.

How To Find the Factors of 519?

You can find the factors of 519 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 519, create a list containing the numbers that are exactly divisible by 519 with zero remainders. One important thing to note is that 1 and 519 are the 519’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 519 are determined as follows:

\[\dfrac{519}{1} = 519\]

\[\dfrac{519}{3} = 173\]

\[\dfrac{519}{519} = 1\]

Therefore, 1, 3, 173, and 519 are the factors of 519.

Total Number of Factors of 519

For 519, there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 519. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the factorization/prime factorization of the given number.
  2. Demonstrate the prime factorization of the number in the form of exponent form.
  3. Add 1 to each of the exponents of the prime factor.
  4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 519 is given as:

Factorization of 519 is 1 x 3 x 173.

The exponent of 1, 3, and 173 is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of 517 is 8. 4 are positive, and 4 factors are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

  • The factor of any given number must be a whole number.
  • The factors of the number cannot be in the form of decimals or fractions.
  • Factors can be positive as well as negative.
  • Negative factors are the additive inverse of the positive factors of a given number.
  • The factor of a number cannot be greater than that number.
  • Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 519 by Prime Factorization

The number 519 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.prime factorization of 519

Before finding the factors of 519 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 519, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 519 can be expressed as:

519 = 3 x 173

Factors of 519 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.Factors of 519 in Pairs

For 519, the factor pairs can be found as:

1 x 519 = 519

3 x 173 = 519 

The possible factor pairs of 519 are given as (1, 519) and (3, 173).

All these numbers in pairs, when multiplied, give 519 as the product.

The negative factor pairs of 519 are given as:

-1 x -519 = 519 

-3 x -173 = 519

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -3, -173, and -519 are called negative factors of 519.

The list of all the factors of 519, including positive as well as negative numbers, is given below.

Factor list of 519: 1, -1, 3, -3, 173, -173, 519, and -519

Factors of 519 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 519 are there?


The total number of Factors of 519 is 8.

Factors of 519 are 1, 3, 173, and 519.

Example 2

Find the factors of 519 using prime factorization.


The prime factorization of 519 is given as:

519 $\div$ 3 = 173 

173 $\div$ 173 = 1 

So the prime factorization of 519 can be written as:

3 x 173 = 519

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