Factors of 209: Prime Factorization, Methods, and Examples

The factors of 209 are the numbers that leave zero as the remainder when 209 is divided from such numbers. These factors can be both negative as well as positive, the only difference between the two is the sign with the factor. 

Factors Of 209

The most common ways to determine these factors are through the division method and prime factorization method. 

Factors of 209

Here are the factors of number 209.

Factors of 209: 1, 11, 19, 209

Negative Factors of 209

The negative factors of 209 are similar to its positive factors, just with a negative sign.

Negative Factors of 209: -1, -11, -19, and -209

Prime Factorization of 209

The prime factorization of 209 is the way of expressing its prime factors in the product form.

Prime Factorization: 11 x 19

In this article, we will learn about the factors of 209 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 209?

The factors of 209 are 1, 11, 19, and 209. All of these numbers are the factors as they do not leave any remainder when divided by 209.

The factors of 209 are classified as prime numbers and composite numbers. The prime factors of the number 209 can be determined using the technique of prime factorization.

How To Find the Factors of 209?

You can find the factors of 209 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 209, create a list containing the numbers that are exactly divisible by 209 with zero remainders. One important thing to note is that 1 and 209 are the 209’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 209 are determined as follows:

\[\dfrac{209}{1} = 209\]

\[\dfrac{209}{11} = 19\]

\[\dfrac{209}{19} = 11\]

\[\dfrac{209}{209} = 1\]

Therefore, 1, 11, 19, and 209 are the factors of 209.

Total Number of Factors of 209

For 209 there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 209. 

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

  1. Find the 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 209 is given as:

Factorization of 209 is 1 x 11 x 19.

The exponent of all factors is 1.

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

Therefore, the total number of factors of 209 is 8. 4 are positive and 4 factors are negative.

Important Notes

Here are some important 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 209 by Prime FactorizationFactor of 209 by Prime Factorization

The number 209 is a composite number. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 209 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 209, start dividing by its smallest 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 209 can be expressed as:

209 = 11 x 19

Factors of 209 in PairsFactor of 209 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 of the given numbers.

For 209, the factor pairs can be found as:

1 x 209 = 209 

11 x 19 = 209 

The possible factor pairs of 209 are given as (1, 209) and (11, 19).

All these numbers in pairs, when multiplied, give 209 as the product.

The negative factor pairs of 209 are given as:

-1 x -209 = 209 

-11 x -19 = 209 

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, -11, -19, and -209 are called negative factors of 209.

The list of all the factors of 209 including positive as well as negative numbers is given below.

Factor list of 209: 1, -1, 11, -11, 19, -19, 209, and -209

Factors of 209 Solved Examples

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

Example 1

How many factors of 209 are there?

Solution

The total number of Factors of 209 is 4.

Factors of 209 are 1, 11, 19, and 209.

Example 2

Find the factors of 209 using prime factorization.

Solution

The prime factorization of 209 is given as:

209 $\div$ 11 = 19 

19 $\div$ 19 = 1 

So the prime factorization of 209 can be written as:

11 x 19 = 209 

Factors of 208|Factors List| Factors of 210