The **factors of
112** are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112 i.e. F_{112} = {1, 2, 4, 7, 8, 14, 16, 28, 56, 112}. The factors of 112 are all the numbers that can divide 112 without leaving a
remainder.

We can check if these
numbers are factors of 112 by dividing 112 by each of them. If the result is a
whole number, then the number is a factor of 112. Let's do this for each of the
numbers listed above:

·
1 is a factor of 112
because 112 divided by 1 is 112.

·
2 is a factor of 112
because 112 divided by 2 is 56.

·
4 is a factor of 112
because 112 divided by 4 is 28.

·
7 is a factor of 112
because 112 divided by 7 is 16.

·
8 is a factor of 112
because 112 divided by 8 is 14.

·
14 is a factor of 112
because 112 divided by 14 is 8.

·
16 is a factor of 112
because 112 divided by 16 is 7.

·
28 is a factor of 112
because 112 divided by 28 is 4.

·
56 is a factor of 112
because 112 divided by 56 is 2.

·
112 is a factor of 112
because 112 divided by 112 is 1.

**How to Find Factors of
112?**

1 and the number
itself are the factors of every number. So, 1 and 112 are two factors of 112.
To find the other factors of 112, we can start by dividing 112 by the numbers
between 1 and 112. If we divide 112 by 2, we get a remainder of 0. Therefore, 2
is a factor of 112. If we divide 112 by 3, we get a remainder of 1. Therefore,
3 is not a factor of 112.

Next, we can check if 4
is a factor of 112. If we divide 112 by 4, we get a remainder of 0. Therefore,
4 is also a factor of 112. We can continue this process for all the possible
factors of 112.

Through this process,
we can find that the factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
These are the only numbers that can divide 112 without leaving a remainder.

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**Properties of the
Factors of 112**

The factors of 112
have some interesting properties. One of the properties is that the sum of the
factors of 112 is equal to 248. We can see this by adding all the factors of 112
together:

1 + 2 + 4 + 7 + 8 + 14
+ 16 + 28 + 56 + 112 = 248

Another property of the
factors of 112 is that the prime factors of 112 are 2, and 7 only.

**Applications of the
Factors of 112**

The factors of 112
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
112 and 120, we need to find the factors of both numbers and identify the
largest factor they have in common. The factors of 112 are 1, 2, 4, 7, 8, 14, 16,
28, 56, and 112. The factors of 120 are 1, 2, 3, 5, 6, 8, 10, 12, 15, 20, 24,
30, 40, 60, and 120. The largest factor that they have in common is 8.
Therefore, the HCF of 112 and 120 is 8.

Another application of
the factors of 112 is in prime factorization. Prime factorization is the
process of expressing a number as the product of its prime factors. The prime
factors of 112 are 2, and 7, since these are the only prime numbers that can
divide 112 without leaving a remainder. Therefore, we can express 112 as:

112 = 2 × 2 × 2 × 2 × 7

We can do prime
factorization by division and factor tree method also. Here is the prime
factorization of 112 by division method,

∴ 112 = 2 × 2 × 2
× 2 × 7

Here is the prime
factorization of 112 by the factor tree method,

∴ 112 = 2 × 2 × 2
× 2 × 7

**Conclusion**

The **factors of
112** are the numbers that can divide 112 without leaving a remainder.
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112. The factors of 112
have some interesting properties, such as having a sum of 248. The factors of 112
have several applications in mathematics, such as finding the highest common
factor and prime factorization.

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