Factors of 109: Prime Factorization, Methods, and Examples

The factors of 109 are the numbers upon which the number 109 is completely divisible. These numbers are only two in existence since 109 is a prime number. So, its factors are the number 1 and the number itself, 109.

Factors Of 109

The factors of 109 can be determined through both the division method and the prime factorization. In both cases, the results yielded for factors are the same.  

Factors of 109

Here are the factors of number 109.

Factors of 109: 1, 109

Negative Factors of 109

The negative factors of 109 are similar to its positive factors, just with a negative sign.

Negative Factors of 109: -1 and -109

Prime Factorization of 109

The prime factorization of 109 is the way of expressing its prime factors in the form of a product.

Prime Factorization: 1 x 109

In this article, we will learn about the factors of 109 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 109?

The factors of 109 are 1 and 109. All of these numbers are the factors as they do not leave any remainder when divided by 109.

The factors of 109 are classified as prime numbers and composite numbers. The prime factors of the number 109 can be determined using the technique of prime factorization.

How To Find the Factors of 109?

You can find the factors of 109 by using the rules of divisibility. The rule of divisibility states that any number when divided by any other natural number then it 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 109, create a list containing the numbers that are exactly divisible by 109 with zero remainders. One important thing to note is that 1 and 109 are 109’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 109 are determined as follows:

\[\dfrac{109}{1} = 109\]

\[\dfrac{109}{109} = 1\]

Therefore, 1 and 109 are the factors of X.

Total Number of Factors of 109

For 109 there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 109. 

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 109 is given as:

The factorization of 109 is 1 x 109.

The exponent of 1 and 109 is 1.

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

Therefore, the total number of factors of 109 is 4, where 2 are positive factors and 2 are negative factors.

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 which is the smallest prime factor.

Factors of 109 by Prime FactorizationFactor of 109 by Prime Factorization

The number 109 is a prime 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 109 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 109, 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 109 can be expressed as:

109 = 1 x 109

Factors of 109 in PairsFactor of 109 in Pairs

The factor pairs are the duplet of numbers that when multiplied together result in the factorized number. Depending upon the total number of factors of the given numbers, factor pairs can be more than one.

For 109, the factor pairs can be found as:

1 x 109 = 109

The possible factor pairs of 109 are given as (1, 109).

All these numbers in pairs, when multiplied, give 109 as the product.

The negative factor pairs of 109 are given as:

-1 x -109 = 109

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 -109 are called negative factors of 109.

The list of all the factors of 109 including positive as well as negative numbers is given below.

Factor list of 109: 1, -1, 109, and -109

Factors of 109 Solved Examples

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

Example 1

How many factors of 109 are there?

Solution

The total number of Factors of 109 is 2.

Factors of 109 are 1 and 109.

Example 2

Find the sum of the factors of 109.

Solution

The factors of 109 are 1 and 109. Their sum is given below:

Sum = 1 + 109 = 110

Factors of 108|Factors List| Factors of 110