119 LearnersLast updated on May 26th, 2025
Factors of 5200
Factors are the numbers that divide any given number evenly without 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 5200, how they are used in real life, and tips to learn them quickly.
What are the Factors of 5200?
The numbers that divide 5200 evenly are known as factors of 5200.
A factor of 5200 is a number that divides the number without remainder.
The factors of 5200 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 25, 40, 52, 65, 80, 104, 130, 160, 208, 260, 325, 520, 650, 1040, 1300, 2600, and 5200.
Negative factors of 5200: -1, -2, -4, -5, -8, -10, -13, -16, -20, -26, -25, -40, -52, -65, -80, -104, -130, -160, -208, -260, -325, -520, -650, -1040, -1300, -2600, and -5200.
Prime factors of 5200: 2, 5, and 13.
Prime factorization of 5200: 24 × 52 × 13.
The sum of factors of 5200: 1 + 2 + 4 + 5 + 8 + 10 + 13 + 16 + 20 + 26 + 25 + 40 + 52 + 65 + 80 + 104 + 130 + 160 + 208 + 260 + 325 + 520 + 650 + 1040 + 1300 + 2600 + 5200 = 14796
How to Find Factors of 5200?
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 5200. Identifying the numbers which are multiplied to get the number 5200 is the multiplication method.
Step 1: Multiply 5200 by 1, 5200 × 1 = 5200.
Step 2: Check for other numbers that give 5200 after multiplying:
2 × 2600 = 5200
4 × 1300 = 5200
5 × 1040 = 5200
8 × 650 = 5200
10 × 520 = 5200
13 × 400 = 5200
Therefore, the positive factor pairs of 5200 are: (1, 5200), (2, 2600), (4, 1300), (5, 1040), (8, 650), (10, 520), (13, 400), etc. 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 the simple division method
Step 1: Divide 5200 by 1, 5200 ÷ 1 = 5200.
Step 2: Continue dividing 5200 by the numbers until the remainder becomes 0.
5200 ÷ 1 = 5200
5200 ÷ 2 = 2600
5200 ÷ 4 = 1300
5200 ÷ 5 = 1040
5200 ÷ 8 = 650
5200 ÷ 10 = 520
Therefore, the factors of 5200 are: 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 25, 40, 52, 65, 80, 104, 130, 160, 208, 260, 325, 520, 650, 1040, 1300, 2600, and 5200.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 5200 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
5200 ÷ 2 = 2600
2600 ÷ 2 = 1300
1300 ÷ 2 = 650
650 ÷ 2 = 325
325 ÷ 5 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
The prime factors of 5200 are 2, 5, and 13.
The prime factorization of 5200 is: 24 × 52 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 5200 is divided by 2 to get 2600.
Step 2: Now divide 2600 by 2 to get 1300.
Step 3: Then divide 1300 by 2 to get 650.
Step 4: Divide 650 by 2 to get 325.
Step 5: Divide 325 by 5 to get 65.
Step 6: Divide 65 by 5 to get 13. Here, 13 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 5200 is: 24 × 52 × 13.
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 5200: (1, 5200), (2, 2600), (4, 1300), (5, 1040), (8, 650), (10, 520), (13, 400), etc.
Negative factor pairs of 5200: (-1, -5200), (-2, -2600), (-4, -1300), (-5, -1040), (-8, -650), (-10, -520), (-13, -400), etc.
Common Mistakes and How to Avoid Them in Factors of 5200
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 5200, 1 and 5200 are also factors.
Mistake 2
Missing Negative Factors
We often only mention positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 5200 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 5200/1.5 = 3466.666..., and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only primes.
For example, thinking all the factors of 5200 are prime numbers.
For example, 2, 5, and 13 are the prime factors of 5200, 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 5200 as 2^4 × 5^2 × 13 and missing all the key factors.
Factors of 5200 Examples
Problem 1
There are 13 friends and 5200 candies. How will they divide it equally?
They will get 400 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
5200/13 = 400
Problem 2
A field is rectangular, the length of the field is 104 meters and the total area is 5200 square meters. Find the width.
50 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
5200 = 104 × width
To find the value of the width, we need to shift 104 to the left side.
5200/104 = width
Width = 50.
Problem 3
There are 25 bags and 5200 apples. How many apples will be in each bag?
Each bag will have 208 apples.
Explanation
To find the apples in each bag, divide the total apples with the bags.
5200/25 = 208
Problem 4
In a class, there are 5200 students, and 65 groups. How many students are there in each group?
There are 80 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
5200/65 = 80
Problem 5
5200 books need to be arranged in 130 shelves. How many books will go on each shelf?
Each of the shelves has 40 books.
Explanation
Divide the total books with shelves.
5200/130 = 40
FAQs on Factors of 5200
1.What are the factors of 5200?
2.Mention the prime factors of 5200.
3.Is 5200 a multiple of 4?
4.Mention the factor pairs of 5200.
5.What is the square of 5200?
6.How can children in United States use numbers in everyday life to understand Factors of 5200?
7.What are some fun ways kids in United States can practice Factors of 5200 with numbers?
8.What role do numbers and Factors of 5200 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 5200 skills?
Important Glossaries for Factor of 5200
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 5200 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 25, 40, 52, 65, 80, 104, 130, 160, 208, 260, 325, 520, 650, 1040, 1300, 2600, and 5200.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 13 are prime factors of 5200.
- 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 5200 are (1, 5200), (2, 2600), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 5200 is 24 × 52 × 13.
- Division method: A method to determine the factors of a number by dividing the number by integers to see if the result is a whole number.
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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.
