Factors of 19 | Prime Factorization of 19 | Factor Tree of 19

Factors of 19:  The factors of a number are a set of numbers that divide a given number equally. The number 19 is a prime number. So, it can only be divided by 1 or by itself. This means, 19 has only two factors, i.e., 1 and 19.

The factors of a number can be written in pairs. They have both positive and negative factors. In this article, we will learn how to find the factors of 19, its prime factorization, and the factor tree. Keep reading to learn more.

What Are the Factors of 19?

The factors of 19 are the numbers that can divide 19 evenly and they do not leave any remainder. Factors of 19 have both positive and negative and they are given in the table below:

Factors of 19: 1 and 19
Negative Factors of 19: -1 and -19
Prime Factorization of 19: 1 X 19 or 19¹
Pair Factors of 19:  (1, 19) and (19, 1)
Prime Factors of 19: 19
Sum of Factors of 19: 20
Sum of Prime Factors of 19: 19

What Are the Factors of 19 in Pairs?

A pair factor of 19 is a combination of two numbers when multiplied together giving the product 19. These pair factors are also written in positive and negative pairs as shown below:

Positive Pair Factors of 19

The positive pair factors of 19 are (1, 19)

Negative Pair Factors of 19

The negative pair factors of 19 are (-1, -19)

How to Find Factors of 19 Using the Division Method?

Let us find the factors of 19 using the division method. We must note that 19 is a prime number. So only two numbers will be completely divisible by it without leaving any remainder. These numbers are 1 and 19. The following steps show how to find the factors of 19 using the division method:

19 ÷ 1 = 19
19 ÷ 19= 1

Hence, the factors of 19 are 1 and 19.

What Is the Prime Factorization of 19?

First, we need to check whether the given number (19) is a prime number. If it is a prime number, it has only two factors: 1 and 19. If the number is a composite number, then it has more than two factors.

19 is a prime number so, its factors are 1 and 19. Thus, there is no need to employ the prime factorization method to find the factors of 19.

Here is a visual representation of the prime factorization of 19, to present a more precise idea.

What Is the Factor Tree of 19?

We can also use the factor tree to find the prime factors of 19. In this method, we will place the number 19 on top. As part of the branches, we will write down any set of pair factors of 19. Since 19 is a prime number, it will end after one step- when we split its factors into 1 and 19.

Step 1: Let us place the number 19 at the top of the factor tree. Now, let’s write down 19 in pairs, 1 and 19.
Step 2: Since they are both prime numbers, we can no longer divide them. This brings us to the end of the factor tree.
There is only one way to write the factor tree of 19. Below is a pictorial representation of the factor tree of 19:

Solved Examples on Multiples of 19

Question 1: How do you find multiples of 19?
Answer: To find multiples of 19, you will have to multiply the number 19 with a sequence of natural numbers. Alternatively, using the repeated addition method, you can find multiples of 19.

Question 2: What are the multiples of 19 between 30 and 350?
Answer: There are a total of 16 multiples for the number 19 between 30 and 350.
And the numbers between 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, 247, 266, 285, 304, 323, and 342 are the 16 multiples between 30 and 350.

Question 3: What is the sum of the first 6 multiples of 19?
Answer: the first 6 multitudes of 19 are: 19, 38, 57, 76, 95, and 114.
19 + 38 + 57 + 76 + 95 + 114 = 399
So, 399 is the sum of the first 6 multitudes of 19.

Question 4: What are the first 9 multiples of 19?
Answer: 19, 38, 57, 76, 95, 114, 133, 152, and 171 are the first 9 multiples of 11.
19 x 1 = 19
19 x 2 = 38
19 x 3 = 57
19 x 4 = 76
19 x 5 = 95
19 x 6 = 114
19 x 7 = 133
19 x 8 = 152
19 x 9 = 171

Question 4: Is 119 a multiple of 19 yes, or no?
Answer: No, since after dividing 119 with 19 leaves a  remainder.

Question 6: Is 361 a multiple of 19 yes, or no?
Answer: yes, 361 is a 19 multiple.
As 19 x 19 = 361.

Question 7: What are multiples of 19 that are less than 400?
Answer: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, 247, 266, 285, 304, 323, 342, 361, 380, and 399 are the 19 multitudes that are less than 400.

Question 7: What are multiples of 19 to 200?
Answer: The multiples of 19 less than 200 are 19, 38, 57, 76, 95, 114, 133, 152, 171, and 190.

FAQs on Multiples of 19

What are the multiples of 19 up to 90?
19, 38, 57, and 76 are the 19 multiples up to 90.

Are the multiples of 19 always even?
Some are even and some are not when it comes to 19 multiples.

What are the common multiples of 19 and 3?
The common multiples of 19 and 3 are 57.

What are 5 multiples of 19?
19, 38, 57, 76, and 95 are the 5 multiples of 19.

We hope this article on Multiples of 19 is helpful to you. If you have any questions related to this post or in general about 19 multiples, ping us through the comment section below and we will get back to you as soon as possible.