Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 12 employees and 3072 tasks. How will they distribute the tasks equally?
They will get 256 tasks each.
To distribute the tasks equally, we need to divide the total tasks by the number of employees.
3072/12 = 256
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.
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.
There are 24 boxes and 3072 apples. How many apples will be in each box?
Each box will have 128 apples.
To find the apples in each box, divide the total apples by the boxes.
3072/24 = 128
In a concert, there are 3072 attendees and 48 sections. How many attendees are in each section?
There are 64 attendees in each section.
Dividing the attendees by the total sections, we will get the number of attendees in each section.
3072/48 = 64
A library has 3072 books and 384 shelves. How many books will go on each shelf?
Each shelf will have 8 books.
Divide total books by the number of shelves.
3072/384 = 8
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.
: She loves to read number jokes and games.