116 LearnersLast updated on May 26th, 2025
Factors of 3072
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 3072, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 3072?
The numbers that divide 3072 evenly are known as factors of 3072.
A factor of 3072 is a number that divides the number without remainder.
The factors of 3072 include 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, and 3072.
Negative factors of 3072: -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -64, -96, -128, -192, -256, -384, -512, -768, -1024, -1536, and -3072.
Prime factors of 3072: 2 and 3.
Prime factorization of 3072: 210 × 3.
The sum of factors of 3072: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 64 + 96 + 128 + 192 + 256 + 384 + 512 + 768 + 1024 + 1536 + 3072 = 9216
How to Find Factors of 3072?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using 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 3072. Identifying the numbers which are multiplied to get the number 3072 is the multiplication method.
Step 1: Multiply 3072 by 1, 3072 × 1 = 3072.
Step 2: Check for other numbers that give 3072 after multiplying:
2 × 1536 = 3072
3 × 1024 = 3072
4 × 768 = 3072
6 × 512 = 3072
8 × 384 = 3072
12 × 256 = 3072
16 × 192 = 3072
24 × 128 = 3072
32 × 96 = 3072
48 × 64 = 3072
Therefore, the positive factor pairs of 3072 are: (1, 3072), (2, 1536), (3, 1024), (4, 768), (6, 512), (8, 384), (12, 256), (16, 192), (24, 128), (32, 96), (48, 64). 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 3072 by 1, 3072 ÷ 1 = 3072.
Step 2: Continue dividing 3072 by the numbers until the remainder becomes 0.
3072 ÷ 1 = 3072
3072 ÷ 2 = 1536
3072 ÷ 3 = 1024
3072 ÷ 4 = 768
3072 ÷ 6 = 512
3072 ÷ 8 = 384
3072 ÷ 12 = 256
3072 ÷ 16 = 192
3072 ÷ 24 = 128
3072 ÷ 32 = 96
3072 ÷ 48 = 64
Therefore, the factors of 3072 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 3072.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 3072 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3072 ÷ 2 = 1536
1536 ÷ 2 = 768
768 ÷ 2 = 384
384 ÷ 2 = 192
192 ÷ 2 = 96
96 ÷ 2 = 48
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
The prime factors of 3072 are 2 and 3.
The prime factorization of 3072 is: 2^10 × 3.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 3072 is divided by 2 to get 1536.
Step 2: Now divide 1536 by 2 to get 768.
Step 3: Then divide 768 by 2 to get 384.
Step 4: Divide 384 by 2 to get 192.
Step 5: Continue dividing by 2 until you reach 6.
Step 6: Divide 6 by 2 to get 3. Here, 3 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 3072 is: 2^10 × 3.
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 3072: (1, 3072), (2, 1536), (3, 1024), (4, 768), (6, 512), (8, 384), (12, 256), (16, 192), (24, 128), (32, 96), (48, 64).
Negative factor pairs of 3072: (-1, -3072), (-2, -1536), (-3, -1024), (-4, -768), (-6, -512), (-8, -384), (-12, -256), (-16, -192), (-24, -128), (-32, -96), (-48, -64).
Common Mistakes and How to Avoid Them in Factors of 3072
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 number. Always remember to include 1 and the number itself.
For example, in factors of 3072, 1 and 3072 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 3072 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 3072/1.5 = 2048, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 3072 are prime numbers.
For example, 2 and 3 are the prime factors of 3072, but it has other factors like 4, 12.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3072 as 2^10 × 3 and missing all the key factors.
Factors of 3072 Examples
Problem 1
There are 12 employees and 3072 tasks. How will they distribute the tasks equally?
They will get 256 tasks each.
Explanation
To distribute the tasks equally, we need to divide the total tasks by the number of employees.
3072/12 = 256
Problem 2
A rectangular garden has an area of 3072 square meters and a length of 32 meters. What is the width of the garden?
96 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
3072 = 32 × width
To find the value of width, we need to shift 32 to the left side.
3072/32 = width
Width = 96.
Problem 3
There are 24 boxes and 3072 apples. How many apples will be in each box?
Each box will have 128 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
3072/24 = 128
Problem 4
In a concert, there are 3072 attendees and 48 sections. How many attendees are in each section?
There are 64 attendees in each section.
Explanation
Dividing the attendees by the total sections, we will get the number of attendees in each section.
3072/48 = 64
Problem 5
A library has 3072 books and 384 shelves. How many books will go on each shelf?
Each shelf will have 8 books.
Explanation
Divide total books by the number of shelves.
3072/384 = 8
FAQs on Factors of 3072
1.What are the factors of 3072?
2.Mention the prime factors of 3072.
3.Is 3072 a multiple of 8?
4.Mention the factor pairs of 3072?
5.What is the square of 3072?
6.How can children in Canada use numbers in everyday life to understand Factors of 3072?
7.What are some fun ways kids in Canada can practice Factors of 3072 with numbers?
8.What role do numbers and Factors of 3072 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 3072 skills?
Important Glossaries for Factors of 3072
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3072 are 1, 2, 3, 4, 6, 8, etc.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 3072.
- 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 3072 are (1, 3072), (2, 1536), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 3072 is 2^10 × 3.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using this method, 2 and 1536 are identified as factors of 3072.
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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.
