211 LearnersLast updated on May 26th, 2025
Factors of 112
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:
- Use of Multiplication Method
- Use of Division Method
- 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).
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.
Mistake 1
Confusing Factors with Multiples
The factors of a number divide the given number without any remainder, whereas multiples are the products of multiplying the number by an integer. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. The multiples are 12, 24, 36, and so on. To avoid this confusion, always understand the two concepts separately.
Factors Of 112 Examples
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?
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.
Problem 2
Raha has 112 pens. She wants to put them in boxes; 7 pens in each box. How many boxes will she need?
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.
Problem 3
What is the GCF of 112 and 56?
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.
FAQs on Factors Of 112
1.What are the multiples of 112?
2.What is the prime factorization of 112?
3.Is 112 a multiple of 7?
4.What is the LCM of 112 and 56?
5.What is the square root of 112?
6.How can children in Qatar use numbers in everyday life to understand Factors of 112?
7.What are some fun ways kids in Qatar can practice Factors of 112 with numbers?
8.What role do numbers and Factors of 112 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 112 skills?
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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About BrightChamps in Qatar
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.
