Factors of 19 Using Prime Factorization
What are the Factors of 19?
The factor of 19 is a number that completely divides 19 and which does not result in a remainder. In this article, we will learn to find the factors of 19 as well as its prime factors and factor pairs.
The number 19 has a total of two factors 1 and 19. Since 19 does not have factors other than 1 and itself, it is known as a prime number.
Factors | Factor Pair | Prime Factorization |
|---|---|---|
1, 19 | (1, 19) | 1 x 19 |
List of Factors of 19
We can find the factors of 19 by applying divisibility rules and basic division facts related to natural numbers.
Number | Is the number a factor of 19 | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of all numbers | 1 \( \times\) 19 = 19 |
2 | No, 19 is not even | --- |
3 | No, 1 + 9 = 10 is not divisible by 3 | --- |
4 | No, 19 \(\div\) 4 = 4 Remainder = 3 | --- |
5 | No, the ones digit is neither 0 nor 5. | --- |
6 | No, 19 is not even and also not divisible by 3 | --- |
7 | No, 19 \(\div\) 7 = 2 and Remainder = 5 | --- |
8 | No, 19 \(\div\) 8 = 2 and Remainder = 3 | --- |
9 | No, 19 \(\div\) 9 = 2 and Remainder = 1 | --- |
10 | No, Ones place digit of 19 is not 0 | --- |
11 | No, 19 \(\div\) 11 = 1 and Remainder = 8 | --- |
12 | No, 19 \(\div\) 12 = 1 and Remainder = 7 | --- |
If we continue to check for numbers greater than 12 we will observe that the multiplication equations will start to repeat. In other words the factor pairs start to repeat, so we can stop checking at this step.
Therefore the factors of 19 are 1 and 19.
[Note: To determine whether a number is a factor of 19 or not, divide 19 by that number and check whether the remainder is zero or not. If the remainder is zero then the number is a factor of 19, otherwise not.]
Prime Factors of 19
The prime factorization of a number is a way of writing the number as the product of prime numbers. The prime numbers multiplied here are then called the prime factors of the original number.
The factor tree below depicts the prime factorization of the number 19.
So, the prime factorization of 19 is given by 1 x 19 and the prime factors of 19 are 1 and 19.
Read More:
Factor Pairs of 19
A factor pair of 19 is a set of its two factors such that their product is 19. A number can have a positive pair of factors and a negative pair of factors.
For example, (1, 19) is a factor pair of 19 as 1 x 19 = 19.
Positive factor of 19 | Positive factor pair of 19 |
|---|---|
1 x 19 = 19 | (1, 19) |
Solved Factors of 19 Examples
Example 1: Find the sum of all factors of 19 and calculate their average.
Solution:
The factors of 19 : 1, 19
Sum of all factors = 1 + 19 = 20
Total number of factors of 19 = 2
Average of factors of 19 = \(\frac{\text{Sum of factors}}{\text{Number of factors}}=\frac{20}{2}=10\)
Hence, the sum of the factors of 19 is 20, and the average of the factors is 10.
Example 2: A contractor buys 19 solar panels. He wants to organize the panels into a rectangular array. How many different arrays can he make?
Solution:
To find the number of arrays the contractor can make find the number of factor pairs of 19
Factors of 19 : 1, 19
So, there is only one factor pair for 19 : (1, 19)
One factor pair can be used to make 2 arrays.
Since there is 1 factor pair so there are two ways to organize the panels in different arrays.
Example 3 : Find the greatest common factor of 19 and 57.
Solution:
To find the greatest common factor of 19 and 57, list the factors of 19 and 57 and select the highest common factor.
Factors of 19 : 1, 19
Factors of 57 : 1, 3, 19, 57
The common factors of 19 and 57 : 1, 19
The greatest of these factors is 19.
Therefore, the greatest common factor of 19 and 57 is 19.
The number 19 has exactly two factors, that is, it does not have factors other than 1 and itself. Hence 19 is not a composite number.
A number which has exactly two factors, that is 1 and the number itself, is known as a prime number.
When 19 is divided by 17 we get 1 as the quotient and 2 as the remainder, that is, the remainder is non-zero. So 19 is not evenly divisible by 17. Hence, 17 is not a factor of 19.
The prime factorization of 19 is:
19 = 1 x 19.