Factors Of 19 | With Easy Division and Prime Factorization

Factors of 19

Numbers that divide 19 exactly without leaving a remainder are called factors of 19. Generally, they are positive or negative. Similar to the pair factors of 19, the negative and positive factors of 19 also exist. 

In the below example, we will represent the pair factor of 19 as (1, 19) or (-1, 19). Alternatively, if we multiply two negative numbers, -1 and -19, the result will be 19.

Using the prime factorization method, we will determine what the factors of 19 are. Afterward, we will evaluate the pair factors of 19.

What are the Factors of 19?

A factor of 19 is any number that divides 19 completely without leaving a remainder. Therefore, the numbers multiplied in pairs, resulting in an original number, are called factors of 19. 

Since the number 19 has only two factors: 1, and the number itself, it is considered a prime number. Thus, 19 has two factors, 1 and 19, and two negative factors, -1 and -19.

Factors of 19: 1 and 19.

Prime Factorization of 19: 19 or 19¹

Pair Factors of 19

Pair factors of 19 are defined as a pair of numbers multiplied together to give a 19. 19 has a positive and a negative pair factor since it is a prime number. Here are the positive and negative factors:

Positive Pair Factors of 19:

Negative Pair Factors of 19:

Thus,  (1, 19) and (-1, -19) are the positive and negative pair factors of 19, respectively.

Factors of 19 by Division Method

Using the division method, we will divide the number 19 by different integers to find out the factors of 19. Integers that divide the original number completely are the factors of 19.

Let’s now look at how to calculate the factors of 19 using the division method.

• 19/1= 19 
• 19/19 = 1 

Whenever a number other than 1 and 19 divides 19, it leaves a remainder. Thus, 1 and 19 are factors of 19.

Prime Factorization of 19

According to the prime factorization method, we will write down “19” as the product of its prime factors. Here are the steps to find prime factors of 19.

Consider a pair factor of 19, say (1, 19)

We cannot factorize it further because factors 1 and 19 are prime numbers. You must write each number as a product of the prime factors.

As a result, 19 is written as 1×19.

Thus, the prime factorization of 19 is 1×19 or 19¹.

Notable: In case a factor is a composite number, break the number into its prime factors, and finally use a product of prime factors to form the number.

Solved Examples

Example 1:

Find the factors that are common to 19 and 24.

Solution:

1 and 19 are factors of 19.

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.

Consequently, 18 and 19 have a common factor of 1.

Example 2:

Find the common factor between 19 and 57.

Solution:

Factors of 19 = 1 and 19.

Factors of 57 = 1, 3, 19, and 7.

  19 and 52 have a common factor of only 1.

Example 3:

Calculate the common factors of 19 and 42.

Solution:

Factors 19 are 1 and 19.

Factors of 42 = 1,2, 3, 6, 7, 14, 21, and 42.

Hence, 19 and 42 have 1 in common.

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