Definition of factors of 17: If a number completely divides 17 with the remainder zero, then that number is called a factor of 17. Thus we can say that the factors of 17 are the divisors of 17. In this section, we will learn about the factors of 17 and the prime factors of 17.
Table of Contents
Highlights of Factors of 17
- 17=1×17 is the prime factorization of 17.
- The factors of 17 are 1 and 17.
- The only prime factor of 17 is 17.
- Negative factors of 17 are -1 and -17.
What are the factors of 17?
To get the factors of 17 we need to first write the number 17 multiplicatively in all possible ways.
| 17 = 1×17 | ∴ 1, 17 are factors of 17 |
This is the only way we can express 17 multiplicatively. Therefore the factors of 17 are the numbers in brown color. So the factors of 17 are 1 and 17.
One knows that -m is a factor of 17 if m is a factor of 17. So we can say that -1 and -17 are the negative factors of 17.
Pair Factors of 17
| 17 = a×b | Factors in Pairs (a,b) |
| 17 = 1×17 | (1, 17) |
Thus the only positive pair factor of 17 is (1, 17).
We know that if (a, b) is a positive pair factor of 17, then (-a, -b) is a negative pair factor of 17. So (-1, -17) is the only negative pair factor of 17.
Number of factors of 17
From above we have calculated the factors of 17 which are 1 and 17. Thus the total number of factors of 17 is two.
Prime Factors of 17
Note that the factors of 17 are 1 and 17. Among those factors, we observe that only 17 is a prime number as it does not have any proper divisors.
∴ the only prime factor of 17 is the number 17 itself.
Also Read:
| Factors of 18: | 1, 2, 3, 6, 9, 18 |
| Factors of 21: | 1, 3, 7, 21 |
| Factors of 26: | 1, 2, 13, 26 |
| Factors of 39: | 1, 3, 13, 39 |
Question: What are the factors of 17?
Video Solution: coming soon…
Is 17 a Prime Number?
As the factors of 17 are 1 and the number itself, by the definition of prime numbers, we can say that 17 is a prime number.
Conclusion: 17 is a prime number.
How to find factors of 17?
Now we will determine the factors of 17 by division method. In this method, we will find the numbers that can divide 17 with no remainder. See that
| 17/1=17 and the remainder is 0 | ∴ 1 and 17 are factors of 17 |
Note that no numbers other than the numbers in violet color can divide 17. So the numbers in violet color, that is, 1 and 17 are the complete list of factors of 17.
This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.