114 LearnersLast updated on May 26th, 2025
Factors of 5120
Factors are the numbers that divide any given number evenly without a 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 5120, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 5120?
The numbers that divide 5120 evenly are known as factors of 5120.
A factor of 5120 is a number that divides the number without a remainder.
The factors of 5120 include 1, 2, 4, 5, 8, 10, 16, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1280, 2560, and 5120.
Negative factors of 5120: -1, -2, -4, -5, -8, -10, -16, -32, -40, -64, -80, -128, -160, -256, -320, -512, -640, -1280, -2560, and -5120.
Prime factors of 5120: 2 and 5.
Prime factorization of 5120: 29 × 5.
The sum of factors of 5120: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 32 + 40 + 64 + 80 + 128 + 160 + 256 + 320 + 512 + 640 + 1280 + 2560 + 5120 = 12768
How to Find Factors of 5120?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 5120. Identifying the numbers which are multiplied to get the number 5120 is the multiplication method.
Step 1: Multiply 5120 by 1, 5120 × 1 = 5120.
Step 2: Check for other numbers that give 5120 after multiplying:
2 × 2560 = 5120
4 × 1280 = 5120
5 × 1024 = 5120
8 × 640 = 5120
Therefore, the positive factor pairs of 5120 are (1, 5120), (2, 2560), (4, 1280), (5, 1024), and (8, 640).
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 5120 by 1, 5120 ÷ 1 = 5120.
Step 2: Continue dividing 5120 by the numbers until the remainder becomes 0.
5120 ÷ 1 = 5120
5120 ÷ 2 = 2560
5120 ÷ 4 = 1280
5120 ÷ 5 = 1024
5120 ÷ 8 = 640
Therefore, the factors of 5120 are 1, 2, 4, 5, 8, 10, 16, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1280, 2560, and 5120.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 5120 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
5120 ÷ 2 = 2560
2560 ÷ 2 = 1280
1280 ÷ 2 = 640
640 ÷ 2 = 320
320 ÷ 2 = 160
160 ÷ 2 = 80
80 ÷ 2 = 40
40 ÷ 2 = 20
20 ÷ 2 = 10
10 ÷ 2 = 5
5 ÷ 5 = 1
The prime factors of 5120 are 2 and 5.
The prime factorization of 5120 is: 29 × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 5120 is divided by 2 to get 2560.
Step 2: Now divide 2560 by 2 to get 1280.
Step 3: Then divide 1280 by 2 to get 640.
Step 4: Divide 640 by 2 to get 320.
Step 5: Divide 320 by 2 to get 160.
Step 6: Divide 160 by 2 to get 80.
Step 7: Divide 80 by 2 to get 40.
Step 8: Divide 40 by 2 to get 20.
Step 9: Divide 20 by 2 to get 10.
Step 10: Divide 10 by 2 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 5120 is: 29 × 5.
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 5120: (1, 5120), (2, 2560), (4, 1280), (5, 1024), (8, 640), (10, 512), (16, 320), (32, 160), (40, 128), (64, 80).
Negative factor pairs of 5120: (-1, -5120), (-2, -2560), (-4, -1280), (-5, -1024), (-8, -640), (-10, -512), (-16, -320), (-32, -160), (-40, -128), (-64, -80).
Common Mistakes and How to Avoid Them in Factors of 5120
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 5120, 1 and 5120 are also factors.
Mistake 2
Missing Negative Factors
We often only mention positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 5120 consist of -1, -2, -4, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 5120/1.5 = 3413.333, 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 5120 are prime numbers.
For example, 2 and 5 are the prime factors of 5120, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 5120 as 2^9 × 5 and missing all the key factors.
Factors of 5120 Examples
Problem 1
There are 64 students and 5120 candies. How many candies will each student get?
Each student will get 80 candies.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students.
5120/64 = 80
Problem 2
A rectangular garden has a length of 640 meters and a total area of 5120 square meters. What is the width?
8 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
5120 = 640 × width
To find the value of width, we need to shift 640 to the left side.
5120/640 = width
Width = 8.
Problem 3
There are 128 bags and 5120 apples. How many apples will be in each bag?
Each bag will have 40 apples.
Explanation
To find the apples in each bag, divide the total apples by the number of bags.
5120/128 = 40
Problem 4
In a school, there are 5120 students, and 320 classes. How many students are there in each class?
There are 16 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
5120/320 = 16
Problem 5
A library has 5120 books and 64 shelves. How many books will go on each shelf?
Each shelf will have 80 books.
Explanation
Divide total books by shelves.
5120/64 = 80
FAQs on Factors of 5120
1.What are the factors of 5120?
2.Mention the prime factors of 5120.
3.Is 5120 a multiple of 10?
4.Mention the factor pairs of 5120?
5.What is the square of 5120?
Important Glossaries for Factors of 5120
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 5120 are 1, 2, 4, 5, 8, 10, 16, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1280, 2560, and 5120.
- Prime factors: The factors which are prime numbers. For example, 2 and 5 are prime factors of 5120.
- 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 5120 are (1, 5120), (2, 2560), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 5120 is 29 × 5.
- Multiple: A number that can be divided by another number without a remainder. For example, 5120 is a multiple of 10.
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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.
