115 LearnersLast updated on May 26th, 2025
Factors of 6500
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 6500, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 6500?
The numbers that divide 6500 evenly are known as factors of 6500.
A factor of 6500 is a number that divides the number without remainder.
The factors of 6500 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 1300, 3250, and 6500.
Negative factors of 6500: -1, -2, -4, -5, -10, -13, -20, -25, -26, -50, -52, -65, -100, -130, -1300, -3250, and -6500.
Prime factors of 6500: 2, 5, and 13.
Prime factorization of 6500: 2² × 5³ × 13.
The sum of factors of 6500: 1 + 2 + 4 + 5 + 10 + 13 + 20 + 25 + 26 + 50 + 52 + 65 + 100 + 130 + 1300 + 3250 + 6500 = 11463
How to Find Factors of 6500?
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 6500. Identifying the numbers which are multiplied to get the number 6500 is the multiplication method.
Step 1: Multiply 6500 by 1, 6500 × 1 = 6500.
Step 2: Check for other numbers that give 6500 after multiplying
2 × 3250 = 6500
4 × 1625 = 6500
5 × 1300 = 6500
10 × 650 = 6500
13 × 500 = 6500
20 × 325 = 6500
25 × 260 = 6500
26 × 250 = 6500
50 × 130 = 6500
52 × 125 = 6500
65 × 100 = 6500
Therefore, the positive factor pairs of 6500 are: (1, 6500), (2, 3250), (4, 1625), (5, 1300), (10, 650), (13, 500), (20, 325), (25, 260), (26, 250), (50, 130), (52, 125), (65, 100).
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 6500 by 1, 6500 ÷ 1 = 6500.
Step 2: Continue dividing 6500 by the numbers until the remainder becomes 0.
6500 ÷ 1 = 6500
6500 ÷ 2 = 3250
6500 ÷ 4 = 1625
6500 ÷ 5 = 1300
6500 ÷ 10 = 650
6500 ÷ 13 = 500
6500 ÷ 20 = 325
6500 ÷ 25 = 260
6500 ÷ 26 = 250
6500 ÷ 50 = 130
6500 ÷ 52 = 125
6500 ÷ 65 = 100
Therefore, the factors of 6500 are: 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 1300, 3250, 6500.
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 factor tree
Using Prime Factorization: In this process, prime factors of 6500 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
6500 ÷ 2 = 3250
3250 ÷ 2 = 1625
1625 ÷ 5 = 325
325 ÷ 5 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
The prime factors of 6500 are 2, 5, and 13.
The prime factorization of 6500 is: 2² × 5³ × 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, 6500 is divided by 2 to get 3250.
Step 2: Now divide 3250 by 2 to get 1625.
Step 3: Then divide 1625 by 5 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 6500 is: 2² × 5³ × 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 6500: (1, 6500), (2, 3250), (4, 1625), (5, 1300), (10, 650), (13, 500), (20, 325), (25, 260), (26, 250), (50, 130), (52, 125), (65, 100).
Negative factor pairs of 6500: (-1, -6500), (-2, -3250), (-4, -1625), (-5, -1300), (-10, -650), (-13, -500), (-20, -325), (-25, -260), (-26, -250), (-50, -130), (-52, -125), (-65, -100).
Common Mistakes and How to Avoid Them in Factors of 6500
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 6500, 1 and 6500 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 6500 include -1, -2, -4, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 6500/1.5 = 4333.333, 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 6500 are prime numbers.
For example, 2, 5, and 13 are the prime factors of 6500, but it has other factors like 4, 10, 20, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 6500 as 2² × 5³ × 13 and missing all the key factors.
Factors of 6500 Examples
Problem 1
There are 13 friends and 6500 coins. How will they divide them equally?
They will get 500 coins each.
Explanation
To divide the coins equally, we need to divide the total coins by the number of friends.
6500/13 = 500
Problem 2
A field is rectangular, the length of the field is 50 meters and the total area is 6500 square meters. Find the width.
130 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
6500 = 50 × width
To find the value of width, we need to shift 50 to the left side.
6500/50 = width
Width = 130.
Problem 3
There are 25 boxes and 6500 candies. How many candies will be in each box?
Each box will have 260 candies.
Explanation
To find the candies in each box, divide the total candies by the boxes.
6500/25 = 260
Problem 4
In a class, there are 100 students, and 13 groups. How many students are there in each group?
There are 500 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
6500/13 = 500
Problem 5
6500 books need to be arranged in 50 shelves. How many books will go on each shelf?
Each of the shelves has 130 books.
Explanation
Divide total books by shelves.
6500/50 = 130
FAQs on Factors of 6500
1.What are the factors of 6500?
2.Mention the prime factors of 6500.
3.Is 6500 a multiple of 10?
4.Mention the factor pairs of 6500?
5.What is the square of 6500?
6.How can children in United States use numbers in everyday life to understand Factors of 6500?
7.What are some fun ways kids in United States can practice Factors of 6500 with numbers?
8.What role do numbers and Factors of 6500 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 6500 skills?
Important Glossaries for Factors of 6500
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 6500 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 1300, 3250, 6500.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 13 are prime factors of 6500.
- 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 6500 are (1, 6500), (2, 3250), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 6500 is 2² × 5³ × 13.
- Multiplication method: A method used to find factors by identifying pairs of numbers that multiply to give the original number. For instance, (1, 6500) is a pair for 6500.
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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.
