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A factor of a number is any integer that divides evenly into that number. When a division leaves no remainder it means that the divisor is a Factor of the dividend. Furthermore, Factors of 13 helps with solving difficult mathematical problems that you might face. Additionally, in this blog, you will also learn about the Factors of 13, their Negative Factors, Factor Pairs, their Sum, Factor Tree and the Factors of 13 by Division Method.
What are the Factors of 13?
In simpler terms, factors of a number are those numbers that divide into that number, leaving no remainder. When it comes to 13, things get interesting. The Factors of 13 are:
- 1
- 13
That is right, 13 has only two factors! This unique property is because 13 is a Prime number. Prime numbers are whole numbers greater than 1 that have exactly two distinct positive factors which are 1 and itself.
Here is why 1 and 13 are the only factors of 13. Imagine dividing 13 by different numbers. Dividing by 1 gives us 13, and dividing 13 by 13 gives us 1. Moreover, any other whole number division of 13 will result in a remainder, hence proving that those numbers are not factors of 13.
Also Read: Factors of 10: Factor Tree, Division Method, Factor Pairs
What is the Sum of the Factors of 13?
Additionally, as you now know the Factors of 13, finding their Sum is a breeze. To find the Sum of the factors, you simply add up all the factors together.
In the case of 13, the Sum would be:
1 + 13 = 14
Thus, the Sum of the Factors of 13 is 14.
Also Read: Factors of 15, Division Method, Factor Pairs and more!
What are the factors of Negative 13?
Factors apply not only to positive integers but also to negative integers. The Factors of negative 13 are identical to the Factors of 13. Here is why:
- Multiplying any Factor of 13 by -1 results in the corresponding negative factor.
- In this case, -1 x 1 = -1, and -1 x 13 = -13.
Therefore, the factors of negative 13 are:
- -1
- -13
Also Read: Factors of 16: Negative Factors, Factor Tree, Pairs and Division Method and more!
What are the Factor Pairs of 13?
Factor Pairs are simply the two factors of a number written together as a pair. As you saw earlier, 13 has only two factors. Hence, the factor pairs of 13 are:
- (1, 13)
- (-1, -13) (considering negative factors as well)
Important Note: When working with Factor pairs, the order does not matter (1, 13) is the same as (13, 1).
Factors of 13 by Division Method
Furthermore, there are different methods to find the factors of a number. Here, you will get to learn the Division method:
- Start with 2: The first potential factor to check is 2, the smallest Prime number after 1.
- Divide 13 by 2.
- Since 13 divided by 2 gives a remainder of 1, you know 2 is not a factor.
- Continue with Odd Numbers: Since 13 is not divisible by 2, you can focus on odd numbers as potential factors.
- Move on to the next odd number, which is 3.
- Divide 13 by 3.
- Again, you get a remainder of 1, hence signifying that 3 is not a factor.
- Systematic Division: Keep dividing 13 by consecutive odd numbers (5, 7, 11, etc.). You will continue to get remainders until you reach.
- Reaching the Factor: Finally, when you divide 13 by 13, you get a quotient of 1 with no remainder. Therefore, this signifies that 13 is a factor of itself.
Thus, through this systematic division process, you have proved that the Factors of 13 are 1 and 13.
Related Blogs
I hope this helps! Did you like learning about the Factors of 13? You also learn about the Factors of 1 to 25! Also, keep reading our blogs to learn more about the Basic Concepts of Maths!