The factors of 13 are the numbers that divide the number 13 completely without leaving any remainder. The factors of 13 can be positive or negative, but they cannot be decimals or fractions. For example, the pair factors of 13 can be (1, 13) or (-1, -13). If we multiply the negative pair factors, it will result in the original number. It means that multiplication of -1 and -13 results in 13. In this article, we are going to learn the list of factors of 13, pair factors and the prime factors of 13 using the division method and the prime factorization method.
Table of Contents:
- What are the Factors of 13?
- Pair Factors of 13
- Factors of 13 by Division Method
- Prime Factorization of 13
- Solved Examples
- FAQs
What are the Factors of 13?
The factors of 13 are the numbers that are multiplied in pairs resulting in the original number 13. In other words, the factors of 13 are the numbers that divide the number 13 without leaving the remainder. As the number 13 is a prime number, it has only two factors, such as one and the number itself. Thus, the factors of 13 are 1 and 13.
Factors of 13: 1 and 13 Prime Factorization of 13: 1 x 13 |
Pair Factors of 13
The pair factor of 13 is a pair of numbers, which on multiplication gives the product value as 13. The pair factor of 13 can be a positive pair as well as a negative pair. Since the number 13 is a prime number, it has only one pair factor. The positive pair factor of 13 is given as follows:
Positive Factors of 13 |
Positive Pair Factors of 13 |
1 × 13 |
(1, 13) |
Similarly, the negative pair factor of 13 is given below:
Negative Factors of 13 |
Negative Pair Factors of 13 |
-1 × -13 |
(-1,-13) |
Factors of 13 by Division Method
The division method is one of the methods of finding the factors of 13. In this division method, we have to find the number which divides 13 exactly without leaving any remainder. Now, start with dividing 13 by 1, and continue dividing the number with their consecutive integers.
- 13/1 = 13 (Remainder is 0 and the factor is 1)
- 13/13 = 1 (Remainder is 0 and the factor is 13)
If we divide 13 by numbers other than 1 and 13, it leaves the remainder. Hence, the factors of 13 are 1 and 13.
Also, read: |
Prime Factorization of 13
The process of writing the number as the product of its prime factors is called the prime factorization method. The prime factorization of 13 is given as follows:
Step 1: Write down the pair factor of 13, say (1, 13)
Step 2: Here, both the numbers 1 and 13 are prime numbers and they cannot be split further. So write down the factors as the product of 1 and 13.
Thus, 13 can be written as 1 x 13
Hence, the prime factorization of 13 is 1 x 13 or 13^{1}.
Examples
Example 1:
Find the common factors of 13 and 26.
Solution:
The factors of 13 are 1 and 13
The factors of 26 are 1, 2, 13 and 26
Therefore, the common factors of 13 and 26 are 1 and 13.
Example 2:
Find the common factors of 13 and 17.
Solution:
Factors of 13 = 1, 13
Factors of 17 = 1, 17.
As both the numbers are prime numbers, it has a factor, such as 1 and the number itself.
Therefore, the common factor of 13 and 17 is 1.
Example 3:
Find the common factors of 13 and 39.
Solution:
The factors of 13 are 1 and 13
The factors of 39 are 1, 3, 13, and 39
Hence, the common factors of 13 and 39 are 1 and 13.
Frequently Asked Questions on Factors of 13
What are the factors of 13?
The factors of 13 are 1 and 13, as 13 is a prime number.
What is the prime factorization of 13?
The prime factorization of 13 is 1 x 13 or 13^{1}.
How many factors does the number 13 have?
The number 13 has only two factors such as 1 and the number itself (i.e) 1 and 13.
What are the positive and negative pair factors of 13?
The positive and negative pair factors of 13 are (1, 13) and (-1, -13), respectively.
Is 3 a factor of 13?
No, 3 is not a factor of 13. Since 13 is a prime number, the factors of 13 are 1 and the number itself.