Definition of factors of 19: If a number completely divides 19 with the remainder zero, then that number is called a factor of 19.
By the above definition, we can say that the factors of 19 are the divisors of 19. In this section, we will learn about the factors of 19 and the prime factors of 19.
Also Read: Basic concepts of the factors of a number
Highlights of Factors of 19
- 19=1×19 is the prime factorization of 19.
- The factors of 19 are 1 and 19.
- The only prime factor of 19 is 19.
- Negative factors of 19 are –1 and –19.
What are the factors of 19?
To get the factors of 19 we need to first write the number 19 multiplicatively in all possible ways.
19 = 1×19
This is the only way we can express 19 multiplicatively. Therefore the factors of 19 in pairs are given as follows:
|19 = a×b||Factors in Pairs (a,b)|
|19 = 1×19||(1, 19)|
Thus the only pair factor of 19 is (1, 19). We know that all the numbers appearing in pair factors are the factors of 19. So we conclude that
The factors of 19 are:
1 and 19.
Number of factors of 19
From above we have calculated the factors of 19 which are 1 and 19. Thus the total number of factors of 19 is two.
Prime Factors of 19
Note that the factors of 19 are 1 and 19. Among those factors, we observe that only 19 is a prime number as it does not have any proper divisors.
∴ the only prime factor of 19 is the number 19 itself.
Question: What are the factors of 19?
Video Solution: coming soon…
Is 19 a Prime Number?
As the factors of 19 are 1 and the number itself, by the definition of prime numbers, we can say that 19 is a prime number.
Conclusion: 19 is a prime number.
How to find factors of 19?
Now we will determine the factors of 19 by division method. In this method, we will find the numbers that can divide 19 with no remainder. See that
19/1=19 and the remainder is 0.
∴ 1 and 19 are factors of 19.
Note that no numbers other than the numbers in violet color can divide 19. So the numbers in violet color, that is, 1 and 19 are the complete list of factors of 19.