The **factors of
13** are 1 and 13 i.e. F_{13} = {1, 13}. The factors of 13 are all the numbers that can divide 13 without leaving a remainder.
13 is a prime number, so it is divisible by 1 and 13 only.

We can check if these
numbers are factors of 13 by dividing 13 by each of them. If the result is a
whole number, then the number is a factor of 13. Let's do this for each of the
numbers listed above:

·
1 is a factor of 13
because 13 divided by 1 is 13.

·
13 is a factor of 13
because 13 divided by 13 is 1.

**Properties of the
Factors of 13**

The factors of 13 have
some interesting properties. One of the properties is that the sum of the
factors of 13 is equal to 14. We can see this by adding all the factors of 13
together:

1 + 13 = 14

Another property of
the factors of 13 is that the only prime factor of 13 is 13 itself.

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**Applications of the
Factors of 13**

The factors of 13 have
several applications in mathematics. One of the applications is in finding the
highest common factor (HCF) of two or more numbers. The HCF is the largest
factor that two or more numbers have in common. For example, to find the HCF of
13 and 26, we need to find the factors of both numbers and identify the largest
factor they have in common. The factors of 13 are 1, and 13. The factors of 26
are 1, 2, 13, and 26. The largest factor that they have in common is 13.
Therefore, the HCF of 13 and 26 is 13.

Another application of
the factors of 13 is in prime factorization. Prime factorization is the process
of expressing a number as the product of its prime factors. The prime factor of
13 is 13 since it is only the prime number that can divide 13 without leaving a
remainder. Therefore, we can express 13 as:

13 = 13

We can do prime
factorization by division method as given below,

∴ 13 = 13

Since 13 is a prime
number, there is no factor tree of 13.

**Conclusion**

The **factors of
13** are the numbers that can divide 13 without leaving a remainder. The
factors of 13 are 1, and 13. The factors of 13 have some interesting
properties, such as having a sum of 14. The factors of 13 have several
applications in mathematics, such as finding the highest common factor and
prime factorization.

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