The **factors of
11** are 1 and 11 i.e. F_{11} = {1, 11}. The factors of 11 are all the numbers that can divide 11 without leaving a remainder.
11 is a prime number, so it is divisible by 1 and 11 only.

We can check if these
numbers are factors of 11 by dividing 11 by each of them. If the result is a
whole number, then the number is a factor of 11. Let's do this for each of the
numbers listed above:

·
1 is a factor of 11
because 11 divided by 1 is 11.

·
11 is a factor of 11
because 11 divided by 11 is 1.

**Properties of the
Factors of 11**

The factors of 11 have
some interesting properties. One of the properties is that the sum of the
factors of 11 is equal to 12. We can see this by adding all the factors of 11
together:

1 + 11 = 12

Another property of
the factors of 11 is that the only prime factor of 11 is 11 itself.

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**Applications of the
Factors of 11**

The factors of 11 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
11 and 22, we need to find the factors of both numbers and identify the largest
factor they have in common. The factors of 11 are 1, and 11. The factors of 22
are 1, 2, 11, and 22. The largest factor that they have in common is 11.
Therefore, the HCF of 11 and 22 is 11.

Another application of
the factors of 11 is in prime factorization. Prime factorization is the process
of expressing a number as the product of its prime factors. The prime factor of
11 is 11 since it is only the prime number that can divide 11 without leaving a
remainder. Therefore, we can express 11 as:

11 = 11

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

∴ 11 = 11

Since 11 is a prime
number, there is no factor tree of 11.

**Conclusion**

The **factors of
11** are the numbers that can divide 11 without leaving a remainder. The
factors of 11 are 1, and 11. The factors of 11 have some interesting
properties, such as having a sum of 12. The factors of 11 have several
applications in mathematics, such as finding the highest common factor and
prime factorization.

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