The **factors of
68** are 1, 2, 4, 17, 34, and 68 i.e. F_{68} = {1, 2, 4, 17,
34, 68}. The factors of 68 are all the numbers that can divide 68 without
leaving a remainder.

We can check if these
numbers are factors of 68 by dividing 68 by each of them. If the result is a
whole number, then the number is a factor of 68. Let's do this for each of the
numbers listed above:

·
1 is a factor of 68
because 68 divided by 1 is 68.

·
2 is a factor of 68
because 68 divided by 2 is 34.

·
4 is a factor of 68
because 68 divided by 4 is 17.

·
17 is a factor of 68
because 68 divided by 17 is 4.

·
34 is a factor of 68
because 68 divided by 34 is 2.

·
68 is a factor of 68
because 68 divided by 68 is 1.

**How to Find Factors of
68?**

1 and the number
itself are the factors of every number. So, 1 and 68 are two factors of 68. To
find the other factors of 68, we can start by dividing 68 by the numbers
between 1 and 68. If we divide 68 by 2, we get a remainder of 0. Therefore, 2
is a factor of 68. If we divide 68 by 3, we get a remainder of 2. Therefore, 3
is not a factor of 68.

Next, we can check if
4 is a factor of 68. If we divide 68 by 4, we get a remainder of 0. Therefore,
4 is also a factor of 68. We can continue this process for all the possible
factors of 68.

Through this process,
we can find that the factors of 68 are 1, 2, 4, 17, 34, and 68. These are the
only numbers that can divide 68 without leaving a remainder.

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**Properties of the
Factors of 68**

The factors of 68 have
some interesting properties. One of the properties is that the sum of the
factors of 68 is equal to 126. We can see this by adding all the factors of 68
together:

1 + 2 + 4 + 17 + 34 + 68
= 126

Another property of
the factors of 68 is that the prime factors of 68 are 2, and 17 only.

**Applications of the
Factors of 68**

The factors of 68 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
68 and 51, we need to find the factors of both numbers and identify the largest
factor they have in common. The factors of 68 are 1, 2, 4, 17, 34, and 68. The
factors of 51 are 1, 3, 17, and 51. The largest factor that they have in common
is 17. Therefore, the HCF of 68 and 51 is 17.

Another application of
the factors of 68 is in prime factorization. Prime factorization is the process
of expressing a number as the product of its prime factors. The prime factors
of 68 are 2, and 17 since these are the only prime numbers that can divide 68
without leaving a remainder. Therefore, we can express 68 as:

68 = 2 × 2 × 17

We can do prime
factorization by division and factor tree method also. Here is the prime
factorization of 68 by division method,

Image 1

∴ 68 = 2 × 2 × 17

Here is the prime
factorization of 68 by the factor tree method,

Image 2

∴ 68 = 2 × 2 × 17

**Conclusion**

The **factors of
68** are the numbers that can divide 68 without leaving a remainder. The
factors of 68 are 1, 2, 4, 17, 34, and 68. The factors of 68 have some
interesting properties, such as having a sum of 126. The factors of 68 have
several applications in mathematics, such as finding the highest common factor
and prime factorization.

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