Factors of 509: Prime Factorization, Methods, and Examples

The number 509 is an odd number because it is not divisible by 2 evenly or completely. 

Factors Of 509

If we see its factors it has only two factors which are 1 and 509 which means it is a prime number.

Factors of 509

Here are the factors of number 509.

Factors of 509: 1, 509

Negative Factors of 509

The negative factors of 509 are similar to its positive aspects, just with a negative sign.

Negative Factors of 509: -1, -509

Prime Factorization of 509

The prime factorization of 509 is the way of expressing its prime factors in the product form.

Prime Factorization: 1 x 509

In this article, we will learn about the factors of 509 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 509?

The factors of 509 are 1 and 509. These numbers are the factors as they do not leave any remainder when divided by 509.

The factors of 509 are classified as prime numbers and composite numbers. The prime factors of the number 509 can be determined using the prime factorization technique.

How To Find the Factors of 509?

You can find the factors of 509 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 509, create a list containing the numbers that are exactly divisible by 509 with zero remainders. One important thing to note is that 1 and 509 are the 509’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 509 are determined as follows:

\[\dfrac{509}{1} = 509\]

\[\dfrac{509}{509} = 1\]

Therefore, 1 and 509 are the factors of 509.

Total Number of Factors of 509

For 509, there are two positive factors and two negative ones. So in total, there are four factors of 509. 

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 509 is given as:

Factorization of 509 is 1 x 509.

The exponent of 1 and 509 is 1.

Adding 1 to each and multiplying them together results in 4.

Therefore, the total number of factors of 509 is four whereas two are positive, and two 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 509 by Prime Factorization

The number 509 is a prime 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 509

Before finding the factors of 509 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 509, 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 509 can be expressed as:

509 = 1 x 509

Factors of 509 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 509 in Pairs

For 509, the factor pairs can be found as:

1 x 509 = 509

The possible factor pairs of 509 is given as (1, 509) 

All these numbers in pairs, when multiplied, give 509 as the product.

The negative factor pairs of 509 are given as:

-1 x -509 = 509

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 and -509 are called negative factors of 509.

The list of all the factors of 509, including positive as well as negative numbers, is given below.

Factor list of 509: 1, -1, 509, and -509

Factors of 509 Solved Examples

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

Example 1

How many factors of 509 are there?


The total number of Factors of 509 is 2.

Factors of 509 are 1 and 509.

Example 2

Find the factors of 509 using prime factorization.


The prime factorization of 509 is given as:

509 $\div$ 509 = 1

So the prime factorization of 509 can be written as:

a x b = 509

Factors of 508|Factors List| Factors of 510