Factors of 112

Factors often come in pairs. There are several methods to figure them out, which you'll be learning about in a second. For now, let's just focus on the factors of 112, which are mentioned below:

Negative factors of 112: -1, -2, -4, -7, -8, -14, -16, -28, -56, -112

Prime factors of 112: 2 and 7

Prime factorization of 112: 2⁴ × 7

The sum of factors of 112: 1 + 2 + 4 + 7 + 8 + 14 +16 + 28 + 56 + 112 = 248
 

For finding factors, school kids use different methods for easy calculation. A few commonly used methods are as follows:

1. Use of Multiplication Method
2. Use of Division Method
3. Use of Prime Factors and Prime Factorization.

So, here we discuss a detailed explanation of the following methods:
 

To find the factors of 112, we will identify pairs of numbers that multiply together to give 112.

Step 1: Start by multiplying two numbers in such a way that the product is 112. 

1 × 112 = 112
2 × 56 = 112
4 × 28 = 112
7 × 16 = 112
8 × 14 = 112

Step 2: The factors of 112 are the numbers obtained from the calculations above.

Step 3: The positive factor pairs of 112 are: (1, 112), (2, 56), (4, 28), (7, 16), and (8, 14).

Step 4: The corresponding negative factor pairs of 112 are: (-1, -112), (-2, -56), (-4, -28), (-7, -16), and (-8, -14).
 

Using this method, we will break down the given number till the remainder is zero. Let us go through the step-by-step process to find the factors of 112:

Step 1: Divide 112 by smaller numbers and see if there is any remainder. E.g., 112/1 = 112. 

Step 2: We will continue in the same way and check for other numbers as well. For 112, the factors are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112. This is because 112 can be divided evenly by these numbers.
 

The prime factors of 112 are 2 and 7. The prime factors can be found using the methods given below:

• Prime Factorization
• Factor Tree

By Using Prime Factorization: It is a method in which we break down a number into its prime factor. 

2 is the smallest prime number, so start dividing with two. And then continue to divide with other prime numbers.

112 ÷ 2 = 56
56 ÷ 2 = 28
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1

 The prime factorization of 112 is :

112 = 2⁴ × 7

With prime factorization, 112 can be broken down into prime factors, 2 and 7.
 

A factor tree is a graphical representation of breaking a composite number into its prime factors. It is an easy method to find out the factors of any number.

Step 1: 112 divided by 2 gives us the quotient 56.

Step 2: Since 56 is not a prime number, it can be divided further.

The prime factorization of 112 is written below : 

 112 = 2⁴ × 7
 

Every number has either a positive or negative factor. Let us look at those sets of factors.

Positive pair Factors: (1,112), (2,56), (4,28), (7,16), and (8,14)

Negative pair Factors:(-1,-112), (-2,-56), (-4,-28), (-7,-16), and (-8,-14)
 

• Factors:  Factors are numbers that divide a given number exactly, without any remainder. For example, 6 is divisible by 1, 2, 3, and 6. Therefore, 1, 2, 3, and 6 are the factors of 6.

• Prime Factors: Prime factors of a number are a set of prime numbers that multiply together to give the original number. For 112, the prime factors are 2 and 7.

• Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).