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 3024, how they are used in real life, and the tips to learn them quickly.
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
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 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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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.
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 friends and 3024 candies. How will they divide it equally?
They will get 252 candies each.
To divide the candies equally, we need to divide the total candies with the number of friends.
3024/12 = 252
A rectangular field has a width of 18 meters and a total area of 3024 square meters. Find the length.
168 meters.
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.
There are 7 boxes and 3024 marbles. How many marbles will be in each box?
Each box will have 432 marbles.
To find the marbles in each box, divide the total marbles with the boxes.
3024/7 = 432
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.
Dividing the students with the total groups, we will get the number of students in each group.
3024/8 = 378
3024 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each of the shelves has 504 books.
Divide total books with shelves.
3024/6 = 504
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.