100 LearnersLast updated on May 26th, 2025
Factors of 1380
Factors are the numbers that divide any given number evenly without a 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 1380, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1380?
The numbers that divide 1380 evenly are known as factors of 1380.
A factor of 1380 is a number that divides the number without remainder.
The factors of 1380 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92, 115, 138, 230, 276, 345, 460, 690, and 1380.
Negative factors of 1380: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -23, -30, -46, -60, -69, -92, -115, -138, -230, -276, -345, -460, -690, and -1380.
Prime factors of 1380: 2, 3, 5, and 23.
Prime factorization of 1380: 2 × 2 × 3 × 5 × 23.
The sum of factors of 1380: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 23 + 30 + 46 + 60 + 69 + 92 + 115 + 138 + 230 + 276 + 345 + 460 + 690 + 1380 = 3960
How to Find Factors of 1380?
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 1380. Identifying the numbers which are multiplied to get the number 1380 is the multiplication method.
Step 1: Multiply 1380 by 1, 1380 × 1 = 1380.
Step 2: Check for other numbers that give 1380 after multiplying
2 × 690 = 1380
3 × 460 = 1380
4 × 345 = 1380
5 × 276 = 1380
6 × 230 = 1380
10 × 138 = 1380
12 × 115 = 1380
15 × 92 = 1380
20 × 69 = 1380
23 × 60 = 1380
30 × 46 = 1380
Therefore, the positive factor pairs of 1380 are: (1, 1380), (2, 690), (3, 460), (4, 345), (5, 276), (6, 230), (10, 138), (12, 115), (15, 92), (20, 69), (23, 60), and (30, 46).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number by 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 1380 by 1, 1380 ÷ 1 = 1380.
Step 2: Continue dividing 1380 by the numbers until the remainder becomes 0.
1380 ÷ 1 = 1380
1380 ÷ 2 = 690
1380 ÷ 3 = 460
1380 ÷ 4 = 345
1380 ÷ 5 = 276
1380 ÷ 6 = 230
1380 ÷ 10 = 138
1380 ÷ 12 = 115
1380 ÷ 15 = 92
1380 ÷ 20 = 69
1380 ÷ 23 = 60
1380 ÷ 30 = 46
Therefore, the factors of 1380 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92, 115, 138, 230, 276, 345, 460, 690, 1380.
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 1380 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
1380 ÷ 2 = 690
690 ÷ 2 = 345
345 ÷ 3 = 115
115 ÷ 5 = 23
23 ÷ 23 = 1
The prime factors of 1380 are 2, 3, 5, and 23.
The prime factorization of 1380 is: 2 × 2 × 3 × 5 × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 1380 is divided by 2 to get 690.
Step 2: Now divide 690 by 2 to get 345.
Step 3: Then divide 345 by 3 to get 115.
Step 4: Divide 115 by 5 to get 23. Here, 23 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1380 is: 2 × 2 × 3 × 5 × 23.
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 1380: (1, 1380), (2, 690), (3, 460), (4, 345), (5, 276), (6, 230), (10, 138), (12, 115), (15, 92), (20, 69), (23, 60), (30, 46).
Negative factor pairs of 1380: (-1, -1380), (-2, -690), (-3, -460), (-4, -345), (-5, -276), (-6, -230), (-10, -138), (-12, -115), (-15, -92), (-20, -69), (-23, -60), (-30, -46).
Common Mistakes and How to Avoid Them in Factors of 1380
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1380, 1 and 1380 are also factors.
Factors of 1380 Examples
Problem 1
There are 23 friends and 1380 candies. How will they divide them equally?
They will get 60 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
1380/23 = 60
Problem 2
A field is rectangular, the length of the field is 30 meters, and the total area is 1380 square meters. Find the width.
46 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1380 = 30 × width
To find the value of width, we need to shift 30 to the left side.
1380/30 = width
Width = 46.
Problem 3
There are 6 containers and 1380 liters of juice. How many liters will be in each container?
Each container will have 230 liters.
Explanation
To find the liters in each container, divide the total liters by the number of containers.
1380/6 = 230
Problem 4
In a class, there are 1380 students and 69 groups. How many students are there in each group?
There are 20 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1380/69 = 20
Problem 5
1380 books need to be arranged in 92 shelves. How many books will go on each shelf?
Each of the shelves has 15 books.
Explanation
Divide total books by shelves.
1380/92 = 15
FAQs on Factors of 1380
1.What are the factors of 1380?
2.Mention the prime factors of 1380.
3.Is 1380 a multiple of 23?
4.Mention the factor pairs of 1380.
5.What is the square of 1380?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 1380?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 1380 with numbers?
8.What role do numbers and Factors of 1380 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 1380 skills?
Important Glossaries for Factors of 1380
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1380 are 1, 2, 3, 4, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 23 are prime factors of 1380.
- 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 1380 are (1, 1380), (2, 690), etc.
- Prime factorization: Breaking down a number into its prime number components. For example, the prime factorization of 1380 is 2 × 2 × 3 × 5 × 23.
- Multiple: A number that can be divided by another without a remainder. For example, 1380 is a multiple of 23.
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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.
