101 LearnersLast updated on May 26th, 2025
Factors of 2112
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 2112, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 2112?
The numbers that divide 2112 evenly are known as factors of 2112.
A factor of 2112 is a number that divides the number without remainder.
The factors of 2112 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 66, 96, 132, 264, 528, 704, 1056, and 2112.
Negative factors of 2112: -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -66, -96, -132, -264, -528, -704, -1056, and -2112.
Prime factors of 2112: 2 and 3.
Prime factorization of 2112: 2^6 × 3 × 11.
The sum of factors of 2112: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 66 + 96 + 132 + 264 + 528 + 704 + 1056 + 2112 = 5088
How to Find Factors of 2112?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 2112. Identifying the numbers which are multiplied to get the number 2112 is the multiplication method.
Step 1: Multiply 2112 by 1, 2112 × 1 = 2112.
Step 2: Check for other numbers that give 2112 after multiplying
2 × 1056 = 2112
3 × 704 = 2112
4 × 528 = 2112
6 × 352 = 2112
8 × 264 = 2112
12 × 176 = 2112
16 × 132 = 2112
24 × 88 = 2112
32 × 66 = 2112
48 × 44 = 2112
Therefore, the positive factor pairs of 2112 are: (1, 2112), (2, 1056), (3, 704), (4, 528), (6, 352), (8, 264), (12, 176), (16, 132), (24, 88), (32, 66), (48, 44).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 2112 by 1, 2112 ÷ 1 = 2112.
Step 2: Continue dividing 2112 by the numbers until the remainder becomes 0.
2112 ÷ 1 = 2112
2112 ÷ 2 = 1056
2112 ÷ 3 = 704
2112 ÷ 4 = 528
2112 ÷ 6 = 352
2112 ÷ 8 = 264
2112 ÷ 12 = 176
2112 ÷ 16 = 132
2112 ÷ 24 = 88
2112 ÷ 32 = 66
2112 ÷ 48 = 44
Therefore, the factors of 2112 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 66, 96, 132, 264, 528, 704, 1056, and 2112.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 2112 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2112 ÷ 2 = 1056
1056 ÷ 2 = 528
528 ÷ 2 = 264
264 ÷ 2 = 132
132 ÷ 2 = 66
66 ÷ 2 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1
The prime factors of 2112 are 2, 3, and 11.
The prime factorization of 2112 is: 2^6 × 3 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 2112 is divided by 2 to get 1056.
Step 2: Now divide 1056 by 2 to get 528.
Step 3: Then divide 528 by 2 to get 264.
Step 4: Divide 264 by 2 to get 132.
Step 5: Divide 132 by 2 to get 66.
Step 6: Divide 66 by 2 to get 33.
Step 7: Divide 33 by 3 to get 11.
Here, 11 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 2112 is: 2^6 × 3 × 11.
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 2112: (1, 2112), (2, 1056), (3, 704), (4, 528), (6, 352), (8, 264), (12, 176), (16, 132), (24, 88), (32, 66), and (48, 44).
Negative factor pairs of 2112: (-1, -2112), (-2, -1056), (-3, -704), (-4, -528), (-6, -352), (-8, -264), (-12, -176), (-16, -132), (-24, -88), (-32, -66), and (-48, -44).
Common Mistakes and How to Avoid Them in Factors of 2112
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every word. Always remember to include 1 and the number itself.
For example, in factors of 2112, 1 and 2112 are also factors.
Factors of 2112 Examples
Problem 1
There are 528 students and 2112 books. How will they divide the books equally?
They will get 4 books each.
Explanation
To divide the books equally, we need to divide the total books by the number of students.
2112/528 = 4
Problem 2
A plot is rectangular, the length of the plot is 64 meters and the total area is 2112 square meters. Find the width?
33 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
2112 = 64 × width
To find the value of width, we need to shift 64 to the left side.
2112/64 = width
Width = 33.
Problem 3
There are 176 chairs and 2112 people. How many people will share each chair?
Each chair will be shared by 12 people.
Explanation
To find how many people will share each chair, divide the total people by the chairs.
2112/176 = 12
Problem 4
In a concert, there are 2112 spectators, and 88 sections. How many spectators are there in each section?
There are 24 spectators in each section.
Explanation
Dividing the spectators by the total sections, we will get the number of spectators in each section.
2112/88 = 24
Problem 5
2112 books need to be arranged in 48 shelves. How many books will go on each shelf?
Each of the shelves has 44 books.
Explanation
Divide total books by shelves.
2112/48 = 44
FAQs on Factors of 2112
1.What are the factors of 2112?
2.Mention the prime factors of 2112.
3.Is 2112 a multiple of 8?
4.Mention the factor pairs of 2112?
5.What is the square of 2112?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 2112?
7.What are some fun ways kids in Vietnam can practice Factors of 2112 with numbers?
8.What role do numbers and Factors of 2112 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 2112 skills?
Important Glossaries for Factor of 2112
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2112 are 1, 2, 3, 4, 6, 8, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 11 are prime factors of 2112.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 2112 are (1, 2112), (2, 1056), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, 2112 = 2^6 × 3 × 11.
- Multiple: A number that can be divided by another number without a remainder. For example, 2112 is a multiple of 8.
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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
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