The **factors of
52** are 1, 2, 4, 13, 26, and 52 i.e. F_{52} = {1, 2, 4, 13, 26, 52}. The factors of 52 are all the numbers that can divide 52 without leaving a remainder.

We can check if these
numbers are factors of 52 by dividing 52 by each of them. If the result is a
whole number, then the number is a factor of 52. Let's do this for each of the
numbers listed above:

·
1 is a factor of 52
because 52 divided by 1 is 52.

·
2 is a factor of 52
because 52 divided by 2 is 26.

·
4 is a factor of 52
because 52 divided by 4 is 13.

·
13 is a factor of 52
because 52 divided by 13 is 4.

·
26 is a factor of 52
because 52 divided by 26 is 2.

·
52 is a factor of 52
because 52 divided by 52 is 1.

**How to Find Factors of
52?**

1 and the number
itself are the factors of every number. So, 1 and 52 are two factors of 52. To
find the other factors of 52, we can start by dividing 52 by the numbers
between 1 and 52. If we divide 52 by 2, we get a remainder of 0. Therefore, 2
is a factor of 52. If we divide 52 by 3, we get a remainder of 1. Therefore, 3
is not a factor of 52.

Next, we can check if
4 is a factor of 52. If we divide 52 by 4, we get a remainder of 0. Therefore,
4 is also a factor of 52. We can continue this process for all the possible
factors of 52.

Through this process,
we can find that the factors of 52 are 1, 2, 4, 13, 26, and 52. These are the
only numbers that can divide 52 without leaving a remainder.

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**Properties of the
Factors of 52**

The factors of 52 have
some interesting properties. One of the properties is that the sum of the
factors of 52 is equal to 98. We can see this by adding all the factors of 52
together:

1 + 2 + 4 + 13 + 26 + 52
= 98

Another property of
the factors of 52 is that the prime factors of 52 are 2 and 13.

**Applications of the
Factors of 52**

The factors of 52 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
52 and 65, we need to find the factors of both numbers and identify the largest
factor they have in common. The factors of 52 are 1, 2, 4, 13, 26, and 52. The
factors of 65 are 1, 5, 13, and 65. The largest factor that they have in common
is 13. Therefore, the HCF of 52 and 65 is 13.

Another application of
the factors of 52 is in prime factorization. Prime factorization is the process
of expressing a number as the product of its prime factors. The prime factors
of 52 are 2 and 13, since these are the only prime numbers that can divide 52
without leaving a remainder. Therefore, we can express 52 as:

52 = 2 × 2 × 13

We can do prime
factorization by division and factor tree method also. Here is the prime
factorization of 52 by division method,

∴ 52 = 2 × 2 × 13

Here is the prime
factorization of 52 by the factor tree method,

∴ 52 = 2 × 2 × 13

**Conclusion**

The **factors of
52** are the numbers that can divide 52 without leaving a remainder. The
factors of 52 are 1, 2, 4, 13, 26, and 52. The factors of 52 have some
interesting properties, such as having a sum of 98. The factors of 52 have
several applications in mathematics, such as finding the highest common factor
and prime factorization.

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