141 LearnersLast updated on May 26th, 2025
Factors of 2600
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 2600, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2600?
The numbers that divide 2600 evenly are known as factors of 2600.
A factor of 2600 is a number that divides the number without remainder.
The factors of 2600 are 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300, and 2600.
Negative factors of 2600: -1, -2, -4, -5, -8, -10, -13, -20, -25, -26, -40, -50, -52, -65, -100, -104, -130, -200, -260, -325, -520, -650, -1300, and -2600.
Prime factors of 2600: 2, 5, and 13.
Prime factorization of 2600: 2³ × 5² × 13.
The sum of factors of 2600: 1 + 2 + 4 + 5 + 8 + 10 + 13 + 20 + 25 + 26 + 40 + 50 + 52 + 65 + 100 + 104 + 130 + 200 + 260 + 325 + 520 + 650 + 1300 + 2600 = 8064
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How to Find Factors of 2600?
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 2600. Identifying the numbers which are multiplied to get the number 2600 is the multiplication method.
Step 1: Multiply 2600 by 1, 2600 × 1 = 2600.
Step 2: Check for other numbers that give 2600 after multiplying
2 × 1300 = 2600
4 × 650 = 2600
5 × 520 = 2600
8 × 325 = 2600
10 × 260 = 2600
13 × 200 = 2600
20 × 130 = 2600
25 × 104 = 2600
26 × 100 = 2600
40 × 65 = 2600
52 × 50 = 2600
Therefore, the positive factor pairs of 2600 are: (1, 2600), (2, 1300), (4, 650), (5, 520), (8, 325), (10, 260), (13, 200), (20, 130), (25, 104), (26, 100), (40, 65), (50, 52).
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 2600 by 1, 2600 ÷ 1 = 2600.
Step 2: Continue dividing 2600 by the numbers until the remainder becomes 0.
2600 ÷ 1 = 2600
2600 ÷ 2 = 1300
2600 ÷ 4 = 650
2600 ÷ 5 = 520
2600 ÷ 8 = 325
2600 ÷ 10 = 260
2600 ÷ 13 = 200
2600 ÷ 20 = 130
2600 ÷ 25 = 104
2600 ÷ 26 = 100
2600 ÷ 40 = 65
2600 ÷ 50 = 52
Therefore, the factors of 2600 are: 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300, 2600.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 2600 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2600 ÷ 2 = 1300
1300 ÷ 2 = 650
650 ÷ 2 = 325
325 ÷ 5 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
The prime factors of 2600 are 2, 5, and 13.
The prime factorization of 2600 is: 2³ × 5² × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 2600 is divided by 2 to get 1300.
Step 2: Now divide 1300 by 2 to get 650.
Step 3: Then divide 650 by 2 to get 325.
Step 4: Divide 325 by 5 to get 65.
Step 5: Divide 65 by 5 to get 13.
Here, 13 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 2600 is: 2³ × 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 2600: (1, 2600), (2, 1300), (4, 650), (5, 520), (8, 325), (10, 260), (13, 200), (20, 130), (25, 104), (26, 100), (40, 65), (50, 52).
Negative factor pairs of 2600: (-1, -2600), (-2, -1300), (-4, -650), (-5, -520), (-8, -325), (-10, -260), (-13, -200), (-20, -130), (-25, -104), (-26, -100), (-40, -65), (-50, -52).
Common Mistakes and How to Avoid Them in Factors of 2600
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 2600, 1 and 2600 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 2600 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 2600/1.5 = 1733.333, 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 2600 are prime numbers.
For example, 2, 5, and 13 are the prime factors of 2600, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 2600 as 2³ × 5² × 13 and missing all the key factors.
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Factors of 2600 Examples
Problem 1
There are 13 friends and 2600 candies. How will they divide it equally?
They will get 200 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
2600/13 = 200
Problem 2
A garden is rectangular, the length of the garden is 40 meters and the total area is 2600 square meters. Find the width?
65 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
2600 = 40 × width
To find the value of width, we need to shift 40 to the left side.
2600/40 = width
Width = 65.
Problem 3
There are 26 baskets and 2600 apples. How many apples will be in each basket?
Each basket will have 100 apples.
Explanation
To find the apples in each basket, divide the total apples by the number of baskets.
2600/26 = 100
Problem 4
In a conference room, there are 520 chairs, and 5 sections. How many chairs are there in each section?
There are 104 chairs in each section.
Explanation
Dividing the chairs by the total sections, we will get the number of chairs in each section.
520/5 = 104
Problem 5
2600 books need to be arranged in 10 shelves. How many books will go on each shelf?
Each of the shelves has 260 books.
Explanation
Divide total books by shelves.
2600/10 = 260
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FAQs on Factors of 2600
1.What are the factors of 2600?
2.Mention the prime factors of 2600.
3.Is 2600 a multiple of 4?
4.Mention the factor pairs of 2600?
5.What is the square of 2600?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 2600?
7.What are some fun ways kids in Vietnam can practice Factors of 2600 with numbers?
8.What role do numbers and Factors of 2600 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 2600 skills?
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Important Glossaries for Factor of 2600
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2600 are 1, 2, 4, 5, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 13 are prime factors of 2600.
- 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 2600 are (1, 2600), (2, 1300), etc.
- Prime factorization: Writing a number as the product of its prime factors. For example, 2³ × 5² × 13 is the prime factorization of 2600.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 2600 is a multiple of 4.
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About BrightChamps in Vietnam
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
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