Factors of 17 Using Prime Factorization
What are the Factors of 17?
A factor of 17 will be a number that divides 17 completely, leaving the remainder as zero. In this article, we will learn to find out the factors of 17 with different methods such as the divisibility method, the prime factorization method and the factor tree method.
The number 17 has a total of two factors, 1 and 17. Since 17 does not have factors other than 1 and itself, it is considered as a prime number.
Factors | Factor Pairs | Prime Factors |
|---|---|---|
1, 17 | (1, 17) | 17 |
List of Factors
The factors of 17 can be obtained using divisibility rules and division facts.
Divisor | Is the number a factor of 17? | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of all numbers | 1 x 17 = 17 |
2 | No, 17 is not even | --- |
3 | No, 1 + 7 = 8 is not divisible by 3 | --- |
4 | No, 17 \(\div\) 4 = 4 Remainder = 1 | --- |
5 | No, the ones digit is neither 0 nor 5. | --- |
6 | No, 17 \(\div\) 6 = 2 Remainder = 5 | --- |
7 | No, 17 \(\div\) 7 = 2 and Remainder = 3 | --- |
8 | No, 17 \(\div\) 8 = 2 and Remainder = 1 | --- |
9 | No, 17 \(\div\) 9 = 1 and Remainder = 8 | --- |
10 | No, 17 \(\div\) 10 = 1 and Remainder = 7 | --- |
11 | No, 17 \(\div\) 11 = 1 and Remainder = 6 | --- |
12 | No, 17 \(\div\) 12 = 1 Remainder = 5 | --- |
The factor list of 17 is just 1 and 17. Since 17 does not have factors other than 1 and itself, 17 is a prime number, as observed earlier.
Factor Pairs
The factor pair of 17 is a set of two factors of 17 such that their product is 17. A number can have a positive and a negative pair of factors.
For example, (1, 17) is the factor pair of 17.
Positive factor of 17 | Positive factor pair of 17 |
|---|---|
1 x 17 = 17 | (1, 17) |
Prime Factors of 17
The factor tree below depicts the prime factorization of the number 17.
So, the prime factorization of 17 is 1 x 17, and the prime factors of 17 are 1 and 17.
The prime factorization of 17 is also calculated as follows:
Start dividing 17 with the smallest prime number and keep on checking with other numbers.
Clearly, the prime factorization of 17 is 1 x 17, and the prime factors of 17 are 1 and 17.
Read More:
Rapid Recall
The factors of 17 are 1 and 17.
Solved Factors of 17 Examples
Example 1: Is 17 a composite number?
Solution:
A composite number has more than two factors. In other words, a composite number must have factors other than 1 and itself.
The factors of 17 are 1 and 17 as was obtained by applying the prime factorization method.
Since 17 does not have a factor other than 1 and itself, it is not a composite number. Instead, it is a prime number.
Example 2: What is the prime number that forms a pair of twin prime numbers with 17?
Solution:
Twin prime numbers have a difference of two between them.
Since one of the prime numbers is 17, the other prime number will be 19 so that difference between 19 and 17 is 2.
Example 3: Sharon is giving out giveaways at her pastry store. She decides to give the giveaways as multiples of 17, starting from Monday and ending on Friday. Make a list of the number of pastries given away from Monday to Friday.
Solution:
The following table shows the number of pastries given away from Monday to Friday.
Days | Number of pastries |
|---|---|
Monday | 17 x 1 = 17 |
Tuesday | 17 x 2 = 34 |
Wednesday | 17 x 3 = 51 |
Thursday | 17 x 4 = 68 |
Friday | 17 x 5 = 85 |
Twin prime numbers between 1 to 50 are:
(3 and 5), (5 and 7), (11 and 13), (17 and 19), (29 and 31) and (41 and 43).
Twin prime numbers are those pairs of prime numbers whose difference should be 2 .
Here, the difference between the given prime numbers is
23 – 11 = 12
So, 11 and 23 are not twin prime numbers.
Two prime numbers are said to be twin prime or prime pairs if they have a difference of 2 between them.
For example, (3 and 5), (5 and 7), (11, 13), (17, 19), and so on.
No, factors must be less than the number itself. The number of factors of any number is limited, that is, finite.