Factors of 17
The factors of 17 are the numbers that divide 17 exactly without leaving any remainder. As 17 is a prime number, it has only two factors. The pair factors of 17 can be positive or negative. For example, the pair factor of 17 can be (1, 17) or (-1, -17). If we multiply the pair of negative numbers, such as multiplying -1 and -17, it will result in the original number 17. Here, we will learn what are the factors of 17, pair factors and the prime factors of 17 using the prime factorization method and many solved examples.
Table of Contents:
- What are the Factors of 17?
- Pair Factors of 17
- Factors of 17 by Division Method
- Prime Factorization of 17
- Solved Examples
- FAQs
What are the Factors of 17?
The numbers that divide 17 completely and leave the remainder 0, then the numbers are the factors of 17. In other words, if two numbers are multiplied together and result in 17, then the numbers are the factors of 17. As 17 is a prime number, it has only two factors, such as 1 and the number itself. Hence, the factors of 17 are 1 and 17.
Factors of 17: 1 and 17. Prime Factorization of 17: 17 or 17^{1}. |
Pair Factors of 17
A pair of numbers that are multiplied together and resulting in 17, then it is called the pair factor of 17. We know that 17 is a prime number and it has one positive pair factor and one negative pair factor. The positive and negative pair factors of 17 are given below:
Positive Pair Factor of 17:
Positive Factors of 17 |
Positive Pair Factors of 17 |
1 × 17 |
(1, 17) |
Negative Pair Factor of 17:
Negative Factors of 17 |
Negative Pair Factors of 17 |
-1 × -17 |
(-1, -17) |
Therefore, the positive and negative pair factors of 17 are (1, 17) and (-1, -17) respectively.
Factors of 17 by Division Method
In the division method, the factors of 17 are found by dividing 17 by different integers. If the integers divide 17 completely without leaving any remainder, then those integers are the factors of 17. Now, let us discuss how to find the factors of 17 by division method.
Now, let’s start dividing 17 by 1 and continue with the other integers.
- 17/1 = 17 (Factor is 1 and Remainder is 0)
- 17/17 = 1 (Factor is 17 and Remainder is 0)
If we divide 17 by any numbers other than 1 and 17, it leaves a remainder value. Hence, the factors of 17 are 1 and 17.
Prime Factorization of 17
In the prime factorization of 17, the number 17 is written as the product of its prime factors. Thus, the process of finding the prime factors of 17 is given below.
Now, take the pair factor of 17, say (1, 17)
Now, check whether the numbers in the pair factors are prime numbers or composite numbers. If a number is a prime number, leave the number as it is. In case, if the numbers in the pair factor are composite numbers, split the numbers into their prime factors, and write those numbers as the product of its prime factors.
We know that the number 1 is neither prime nor composite and hence it cannot split further.
Now, take the other number 17, which is also a prime number.
Hence, 17 is written as the product of 1 and 17.
(i.e.) 17 = 1 × 17.
Therefore, the prime factorization of 17 is 17 or 17^{1}.
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Examples
Example 1:
Find the common factors of 17 and 16.
Solution:
The factors of 17 are 1 and 17.
The factors of 16 are 1, 2, 4, 8 and 16.
Thus, the common factor of 17 and 16 is 1.
Example 2:
Find the common factors of 17 and 18.
Solution:
Factors of 17 = 1 and 17
Factors of 18 = 1, 2, 3, 6, 9 and 18.
As 17 is a prime number, the common factor of 17 and 18 is 1.
Example 3:
Find the common factors of 17 and 11.
Solution:
The factors of 17 are 1 and 17.
The factors of 11 are 1 and 11.
As both the numbers 17 and 11 are prime numbers, the common factor of 17 and 11 is 1.
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Frequently Asked Questions on Factors of 17
What are the factors of 17?
The factors of 17 are 1 and 17, as 17 is a prime number.
What is the prime factorization of 17?
The prime factorization of 17 is 17^{1}.
What are the positive and negative pair factors of 17?
The positive and negative pair factors of 17 are (1, 17) and (-1, -17) respectively.
What is the sum of factors of 17?
The sum of factors of 17 is 18. We know that the factors of 17 are 1 and 17.
Hence, the sum of factors of 17 = 1+17 = 18.
Is 7 a factor a 17?
No, 7 is not a factor of 17. As 17 is a prime number, it has only two such as 1 and 17.