101 LearnersLast updated on May 26th, 2025
Factors of 1300
Factors are the numbers that divide any given number evenly without 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 1300, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1300?
The numbers that divide 1300 evenly are known as factors of 1300.
A factor of 1300 is a number that divides the number without remainder.
The factors of 1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, and 1300.
Negative factors of 1300: -1, -2, -4, -5, -10, -13, -20, -25, -26, -50, -52, -65, -100, -130, -260, -325, -650, and -1300.
Prime factors of 1300: 2, 5, and 13. Prime factorization of 1300: 22 × 52 × 13.
The sum of factors of 1300: 1 + 2 + 4 + 5 + 10 + 13 + 20 + 25 + 26 + 50 + 52 + 65 + 100 + 130 + 260 + 325 + 650 + 1300 = 2958
How to Find Factors of 1300?
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 1300. Identifying the numbers which are multiplied to get the number 1300 is the multiplication method.
Step 1: Multiply 1300 by 1, 1300 × 1 = 1300.
Step 2: Check for other numbers that give 1300 after multiplying
- 2 × 650 = 1300
- 4 × 325 = 1300
- 5 × 260 = 1300
- 10 × 130 = 1300
- 13 × 100 = 1300
- 20 × 65 = 1300
- 25 × 52 = 1300
- 26 × 50 = 1300
Therefore, the positive factor pairs of 1300 are: (1, 1300), (2, 650), (4, 325), (5, 260), (10, 130), (13, 100), (20, 65), (25, 52), and (26, 50).
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 1300 by 1, 1300 ÷ 1 = 1300.
Step 2: Continue dividing 1300 by the numbers until the remainder becomes 0.
- 1300 ÷ 1 = 1300
- 1300 ÷ 2 = 650
- 1300 ÷ 4 = 325
- 1300 ÷ 5 = 260
- 1300 ÷ 10 = 130
- 1300 ÷ 13 = 100
- 1300 ÷ 20 = 65
- 1300 ÷ 25 = 52
- 1300 ÷ 26 = 50
Therefore, the factors of 1300 are: 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, and 1300.
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 1300 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
- 1300 ÷ 2 = 650
- 650 ÷ 2 = 325
- 325 ÷ 5 = 65
- 65 ÷ 5 = 13
- 13 ÷ 13 = 1
The prime factors of 1300 are 2, 5, and 13.
The prime factorization of 1300 is: \(22 \times 52 \times 13\).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 1300 is divided by 2 to get 650.
Step 2: Now divide 650 by 2 to get 325.
Step 3: Then divide 325 by 5 to get 65.
Step 4: Divide 65 by 5 to get 13.
Here, 13 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1300 is: \(22 \times 52 \times 13\).
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 1300: (1, 1300), (2, 650), (4, 325), (5, 260), (10, 130), (13, 100), (20, 65), (25, 52), and (26, 50).
Negative factor pairs of 1300: (-1, -1300), (-2, -650), (-4, -325), (-5, -260), (-10, -130), (-13, -100), (-20, -65), (-25, -52), and (-26, -50).
Common Mistakes and How to Avoid Them in Factors of 1300
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 1300, 1 and 1300 are also factors.
Factors of 1300 Examples
Problem 1
There are 13 friends and 1300 candies. How will they divide it equally?
They will get 100 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
1300/13 = 100
Problem 2
A rectangular garden has a length of 20 meters and a total area of 1300 square meters. Find the width?
65 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1300 = 20 × width
To find the value of width, we need to shift 20 to the left side.
1300/20 = width
Width = 65.
Problem 3
There are 10 baskets and 1300 apples. How many apples will be in each basket?
Each basket will have 130 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
1300/10 = 130
Problem 4
In a conference, there are 1300 attendees and 25 groups. How many attendees are there in each group?
There are 52 attendees in each group.
Explanation
Dividing the attendees by the total groups, we will get the number of attendees in each group.
1300/25 = 52
Problem 5
1300 books need to be arranged in 52 shelves. How many books will go on each shelf?
Each of the shelves has 25 books.
Explanation
Divide total books by shelves. 1300/52 = 25
FAQs on Factors of 1300
1.What are the factors of 1300?
2.Mention the prime factors of 1300.
3.Is 1300 a multiple of 10?
4.Mention the factor pairs of 1300?
5.What is the square of 1300?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 1300?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 1300 with numbers?
8.What role do numbers and Factors of 1300 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of 1300 skills?
Important Glossaries for Factor of 1300
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, and 1300.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 13 are prime factors of 1300.
- 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 1300 are (1, 1300), (2, 650), etc.
- Multiplication method: A technique to find factors by multiplying pairs of numbers to obtain the original number.
- Division method: A method of finding factors by dividing the original number by integers to see which give a whole number result without remainder.
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About BrightChamps in United Arab Emirates
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.
