Factors of 112
2026-02-28 23:14 Diff
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Last updated on December 11, 2025

A factor of a number is any integer that divides the number exactly, leaving no remainder. The concept of factors is applied in many real-life situations, such as determining optimal schedules for work shifts and events.

What are the 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
 

How to Find the Factors of 112?

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:
 

Finding Factors Using Multiplication Method

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).
 

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Finding Factors Using Division Method

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.
 

Prime Factors and Prime Factorization

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.
 

Factor Tree

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
 

Factor Pairs

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)
 

Common Mistakes and How to Avoid Them in Factors Of 112

Children tend to make mistakes while finding the factors of a number. Let us look at how to avoid those mistakes.
 

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Problem 1

Sana wants to arrange 112 books on the shelf into rows, with 4 books in each row. How many rows can Sana make?

Okay, lets begin

Sana can make 28 rows.
 

Explanation

Divide the total number of books by the number of books in each row. 


112 ÷ 4 = 28


Therefore, she can make 28 rows with 4 books in each row. 
 

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Problem 2

Raha has 112 pens. She wants to put them in boxes; 7 pens in each box. How many boxes will she need?

Okay, lets begin

Raha will need 16 boxes.


112 ÷ 7 = 16
 

Explanation

 Raha divides the total number of pens by the number of pens in each box. Therefore, she needs 16 boxes to put 7 pens in each box.
 

Well explained 👍

Problem 3

What is the GCF of 112 and 56?

Okay, lets begin

The GCF of 112 and 56 is 56.
 

Explanation

 The following steps will help to find the GCF of 112 and 56.


Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112


Factors of 56: 1, 2, 4, 7, 8, 14, 28, and 56


Common factors: 1, 2, 4, 7, 8, 14, 28, 56 


GCF of 112 and 56 is 56.
 

Well explained 👍

FAQs on Factors Of 112

1.What are the multiples of 112?

 Multiples are the numbers that we get after multiplying 112 with whole numbers. For example, the multiples of 112 are 112 (1×112), 224 (2×112), 336 (3×112), 448 (4×112), and so on.
 

2.What is the prime factorization of 112?

The prime factors of 112 are 2 and 7. The prime factorization of 112 is 24 × 7. This means that 112 is the product of 2 x 2 x 2 x 2 and 7.

3.Is 112 a multiple of 7?

 Yes, 112 is a multiple of 7. When we multiply 7 × 16 we get 112 as the product.

4.What is the LCM of 112 and 56?

5.What is the square root of 112?

Important Glossaries For Factors Of 112

  • 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).
     

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.