129 LearnersLast updated on May 26th, 2025
Factors of 3024
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 3024, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 3024?
The numbers that divide 3024 evenly are known as factors of 3024.
A factor of 3024 is a number that divides the number without remainder.
The factors of 3024 include 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 126, 168, 189, 252, 336, 378, 504, 756, 1008, 1512, and 3024.
Negative factors of 3024: -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -16, -18, -21, -24, -28, -36, -42, -48, -56, -63, -72, -84, -126, -168, -189, -252, -336, -378, -504, -756, -1008, -1512, and -3024.
Prime factors of 3024: 2, 3, and 7.
Prime factorization of 3024: 24 × 33 × 7.
The sum of factors of 3024: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 16 + 18 + 21 + 24 + 28 + 36 + 42 + 48 + 56 + 63 + 72 + 84 + 126 + 168 + 189 + 252 + 336 + 378 + 504 + 756 + 1008 + 1512 + 3024 = 9360
How to Find Factors of 3024?
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 3024. Identifying the numbers which are multiplied to get the number 3024 is the multiplication method.
Step 1: Multiply 3024 by 1, 3024 × 1 = 3024.
Step 2: Check for other numbers that give 3024 after multiplying:
2 × 1512 = 3024
3 × 1008 = 3024
4 × 756 = 3024
6 × 504 = 3024
Therefore, the positive factor pairs of 3024 are: (1, 3024), (2, 1512), (3, 1008), (4, 756), (6, 504), and so on. 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 3024 by 1, 3024 ÷ 1 = 3024.
Step 2: Continue dividing 3024 by the numbers until the remainder becomes 0.
3024 ÷ 1 = 3024
3024 ÷ 2 = 1512
3024 ÷ 3 = 1008
3024 ÷ 4 = 756
3024 ÷ 6 = 504
Therefore, the factors of 3024 include: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 126, 168, 189, 252, 336, 378, 504, 756, 1008, 1512, and 3024.
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 3024 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3024 ÷ 2 = 1512
1512 ÷ 2 = 756
756 ÷ 2 = 378
378 ÷ 2 = 189
189 ÷ 3 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of 3024 are 2, 3, and 7.
The prime factorization of 3024 is: 2^4 × 3^3 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 3024 is divided by 2 to get 1512.
Step 2: Now divide 1512 by 2 to get 756.
Step 3: Then divide 756 by 2 to get 378.
Step 4: Divide 378 by 2 to get 189.
Step 5: Divide 189 by 3 to get 63.
Step 6: Divide 63 by 3 to get 21.
Step 7: Divide 21 by 3 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 3024 is: 2^4 × 3^3 × 7.
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 3024: (1, 3024), (2, 1512), (3, 1008), (4, 756), (6, 504), and so on.
Negative factor pairs of 3024: (-1, -3024), (-2, -1512), (-3, -1008), (-4, -756), (-6, -504), and so on.
Common Mistakes and How to Avoid Them in Factors of 3024
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 3024, 1 and 3024 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 3024 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add a fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 3024/1.5 = 2016, 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 3024 are prime numbers.
For example, 2, 3, and 7 are the prime factors of 3024, 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 3024 as 2^4 × 3^3 × 7 and missing all the key factors.
Factors of 3024 Examples
Problem 1
There are 12 friends and 3024 candies. How will they divide it equally?
They will get 252 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
3024/12 = 252
Problem 2
A rectangular field has a width of 18 meters and a total area of 3024 square meters. Find the length.
168 meters.
Explanation
To find the length of the field, we use the formula:
Area = length × width
3024 = 18 × length
To find the value of length, we need to shift 18 to the left side.
3024/18 = length
Length = 168.
Problem 3
There are 7 boxes and 3024 marbles. How many marbles will be in each box?
Each box will have 432 marbles.
Explanation
To find the marbles in each box, divide the total marbles with the boxes.
3024/7 = 432
Problem 4
In a class, there are 3024 students, and 8 groups. How many students are there in each group?
There are 378 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
3024/8 = 378
Problem 5
3024 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each of the shelves has 504 books.
Explanation
Divide total books with shelves.
3024/6 = 504
FAQs on Factors of 3024
1.What are the factors of 3024?
2.Mention the prime factors of 3024.
3.Is 3024 a multiple of 8?
4.Mention the factor pairs of 3024?
5.What is the square of 3024?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 3024?
7.What are some fun ways kids in United Kingdom can practice Factors of 3024 with numbers?
8.What role do numbers and Factors of 3024 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 3024 skills?
Important Glossaries for Factor of 3024
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3024 include 1, 2, 3, 4, 6, and so on.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 3024.
- 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 3024 are (1, 3024), (2, 1512), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 3024 is 24 × 33 × 7.
- Multiplication method: A method to find factor pairs by identifying pairs of numbers that multiply to give the original number. For example, identifying 2 × 1512 as a factor pair of 3024.
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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.
