117 LearnersLast updated on May 26th, 2025
Factors of 5040
Factors are the numbers that divide a given number evenly without a 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 5040, how they are used in real life, and tips to learn them quickly.
What are the Factors of 5040?
The numbers that divide 5040 evenly are known as factors of 5040.
A factor of 5040 is a number that divides the number without a remainder.
The factors of 5040 include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 168, 180, 210, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, and 5040.
Negative factors of 5040: -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -12, -14, -15, -16, -18, -20, -21, -24, -28, -30, -35, -36, -40, -42, -45, -56, -60, -63, -70, -72, -80, -84, -90, -105, -112, -120, -126, -140, -168, -180, -210, -252, -280, -315, -336, -360, -420, -504, -560, -630, -720, -840, -1008, -1260, -1680, -2520, and -5040.
Prime factors of 5040: 2, 3, 5, and 7.
Prime factorization of 5040: 24 × 3^2 × 5 × 7.
The sum of factors of 5040 is a large number, calculated by summing all its factors.
How to Find Factors of 5040?
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 5040. Identifying the numbers which are multiplied to get the number 5040 is the multiplication method.
Step 1: Multiply 5040 by 1, 5040 × 1 = 5040.
Step 2: Check for other numbers that give 5040 after multiplying. Some of the factor pairs include:
1 × 5040 = 5040
2 × 2520 = 5040
3 × 1680 = 5040
4 × 1260 = 5040
5 × 1008 = 5040
Therefore, the positive factor pairs of 5040 include: (1, 5040), (2, 2520), (3, 1680), (4, 1260), (5, 1008), etc.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by 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 5040 by 1, 5040 ÷ 1 = 5040.
Step 2: Continue dividing 5040 by numbers until the remainder becomes 0.
5040 ÷ 1 = 5040
5040 ÷ 2 = 2520
5040 ÷ 3 = 1680
5040 ÷ 4 = 1260
5040 ÷ 5 = 1008
Therefore, the factors of 5040 include: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on.
Prime Factors and Prime Factorization
The factors can be found by dividing the number 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 5040 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
5040 ÷ 2 = 2520
2520 ÷ 2 = 1260
1260 ÷ 2 = 630
630 ÷ 2 = 315
315 ÷ 3 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 5040 are 2, 3, 5, and 7.
The prime factorization of 5040 is: 24 × 32 × 5 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 5040 is divided by 2 to get 2520.
Step 2: Now divide 2520 by 2 to get 1260.
Step 3: Then divide 1260 by 2 to get 630.
Step 4: Divide 630 by 2 to get 315.
Step 5: Divide 315 by 3 to get 105.
Step 6: Divide 105 by 3 to get 35. Step 7: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 5040 is: 24 × 32 × 5 × 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 5040 include: (1, 5040), (2, 2520), (3, 1680), and so on.
Negative factor pairs of 5040 include: (-1, -5040), (-2, -2520), (-3, -1680), and so on.
Common Mistakes and How to Avoid Them in Factors of 5040
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 5040, 1 and 5040 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 5040 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 5040/1.5 ≠ 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 5040 are prime numbers. While 2, 3, 5, and 7 are the prime factors of 5040, it has other factors like 4, 6, 8, 9, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 5040 as 24 × 32 × 5 × 7 and missing key factors.
Factors of 5040 Examples
Problem 1
There are 42 students and 5040 pencils. How will they distribute them equally?
They will get 120 pencils each.
Explanation
To distribute the pencils equally, we need to divide the total pencils by the number of students.
5040/42 = 120
Problem 2
A garden is rectangular, with a length of 35 meters and a total area of 5040 square meters. Find the width.
144 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
5040 = 35 × width
To find the value of width, we need to shift 35 to the left side.
5040/35 = width
Width = 144.
Problem 3
There are 35 boxes and 5040 marbles. How many marbles will be in each box?
Each box will have 144 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
5040/35 = 144
Problem 4
In a school, there are 5040 students, and 70 classes. How many students are in each class?
There are 72 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
5040/70 = 72
Problem 5
5040 chairs need to be arranged in 56 rows. How many chairs will go in each row?
Each row will have 90 chairs.
Explanation
Divide the total chairs by the number of rows.
5040/56 = 90
FAQs on Factors of 5040
1.What are the factors of 5040?
2.Mention the prime factors of 5040.
3.Is 5040 a multiple of 9?
4.Mention the factor pairs of 5040?
5.What is the square of 5040?
Important Glossaries for Factors of 5040
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 5040 include 1, 2, 3, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 5040.
- 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 5040 include (1, 5040), (2, 2520), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, 2^4 × 3^2 × 5 × 7 for 5040.
- Division method: A technique used to find factors by dividing the number by integers to see if the remainder is zero. For example, dividing 5040 by 2 gives 2520, indicating both are factors.
Explore More numbers
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.
