The factors of 112 are the numbers that divide 112 completely without leaving a remainder. The factors and the pair factors of 112 can be represented in positive and negative form. For example, the pair factor of 112 can be expressed as (1, 112) or (-1, -112). If we multiply a pair of negative factors, such as multiplying -1 and -112, it will result in an original number 112. In this article, we will learn the factors of 112, pair factors and the prime factors of 112 using the prime factorization method and many solved examples.
Table of Contents:
- What are the Factors of 112?
- Pair Factors of 112
- Factors of 112 by Division Method
- Prime Factorization of 112
- Solved Examples
- FAQs
What are the Factors of 112?
The numbers that divide 112 exactly and leave a remainder 0 are the factors of 112. In other words, the numbers which are multiplied in pairs, resulting in the number 112, are the factors of 112. As the number 112 is an even composite number, it has more than two factors. Hence, the factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56 and 112. Similarly, the negative factors of 112 are -1, -2, -4, -7, -8, -14, -16, -28, -56 and -112.
Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56 and 112. Prime Factorization of 112: 2 × 2 × 2 × 2 × 7 or 2^{4} × 7. |
Pair Factors of 112
A pair of numbers multiplied together, resulting in the original number 112, are the pair factors of 112. As 112 is a composite number, it has more than one pair factor. The positive and negative pair factors of 112 are given below:
Positive Pair Factors of 112:
Positive Factors of 112 |
Positive Pair Factors of 112 |
1 × 112 |
(1, 112) |
2 × 56 |
(2, 56) |
4 × 28 |
(4, 28) |
7 × 16 |
(7, 16) |
8 × 14 |
(8, 14) |
Hence, the positive pair factors of 112 are (1, 112), (2, 56), (4, 28), (7, 16) and (8, 14).
Negative Pair Factors of 112:
Negative Factors of 112 |
Negative Pair Factors of 112 |
-1 × -112 |
(-1, -112) |
-2 × -56 |
(-2, -56) |
-4 × -28 |
(-4, -28) |
-7 × -16 |
(-7, -16) |
-8 × -14 |
(-8, -14) |
Hence, the negative pair factors of 112 are (-1, -112), (-2, -56), (-4, -28), (-7, -16) and (-8, -14).
Factors of 112 by Division Method
The factors of 112 are found using the division method. In this method, the number 112 is divided by different integers. If the integers divide 112 entirely and leave a remainder 0, then those integers are the factors of 112. Now, let us start dividing 112 by one and continue with the different integers.
- 112/1 = 112 (Factor is 1 and Remainder is 0)
- 112/2 = 56 (Factor is 2 and Remainder is 0)
- 112/4 = 28 (Factor is 4 and Remainder is 0)
- 112/7 = 16 (Factor is 7 and Remainder is 0)
- 112/8 = 14 (Factor is 8 and Remainder is 0)
- 112/14 = 8 (Factor is 14 and Remainder is 0)
- 112/16 = 7 (Factor is 16 and Remainder is 0)
- 112/28 = 4 (Factor is 28 and Remainder is 0)
- 112/56 = 2 (Factor is 56 and Remainder is 0)
- 112/112 = 1 (Factor is 112 and Remainder is 0)
If we divide 112 by any numbers other than 1, 2, 4, 7, 8, 14, 16, 28, 56 and 112, it leaves a remainder of some values. Hence, the factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56 and 112.
Prime Factorization of 112
The process of writing the number 112 as the product of its prime factors is called the prime factorization method. Go through the following procedure to find the prime factors of 112.
Take a pair factor of 112, say (1, 112)
Here, factor 1 is neither prime nor composite, and it cannot be factored further.
Now, take the other factor, say 112, which is an even composite number. Hence, 112 can be further factored into its prime factors.
Thus, the number 112 is factored as the product of 7 and 16.
Now, 7 is a prime number, and 16 is a composite number, which is further as 2 × 2 × 2 × 2.
So, 112 is written as 2 × 2 × 2 × 2 × 7.
Therefore, the prime factorization of 112 is 2 × 2 × 2 × 2 × 7 or 2^{4} × 7.
Solved Examples
Example 1:
Find the common factors of 112 and 111.
Solution:
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
The factors of 111 are 1, 3, 37 and 111.
Hence, the common factor of 112 and 111 is 1.
Example 2:
Find the common factors of 112 and 113.
Solution:
Factors of 112 = 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
Factors of 113 = 1 and 113.
As 113 is a prime number, the common factor of 112 and 113 is 1.
Example 3:
Find the common factors of 112 and 110.
Solution:
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
The factors of 110 are 1, 2, 5, 10, 11, 22, 55 and 110.
Hence, the common factors of 112 and 110 are 1 and 2.
Frequently Asked Questions on Factors of 112
What are the factors of 112?
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
What is the prime factorization of 112?
The prime factorization of 112 is 2 × 2 × 2 × 2 × 7 or 2^{4} × 7.
What are the positive pair factors of 112?
The positive pair factors of 112 are (1, 112), (2, 56), (4, 28), (7, 16) and (8, 14).
What are the negative pair factors of 112?
The negative pair factors of 112 are (-1, -112), (-2, -56), (-4, -28), (-7, -16) and (-8, -14).
Is 28 a factor of 112?
Yes, 28 is a factor of 112. As 28 divides 112 exactly and leaves a remainder 0, 28 is a factor of 112.