123 LearnersLast updated on May 26th, 2025
Factors of 1365
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 1365, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1365?
The numbers that divide 1365 evenly are known as factors of 1365.
A factor of 1365 is a number that divides the number without a remainder.
The factors of 1365 are 1, 3, 5, 7, 13, 21, 35, 39, 65, 91, 195, 273, 455, and 1365.
Negative factors of 1365: -1, -3, -5, -7, -13, -21, -35, -39, -65, -91, -195, -273, -455, -1365.
Prime factors of 1365: 3, 5, 7, and 13.
Prime factorization of 1365: 3 × 5 × 7 × 13.
The sum of factors of 1365: 1 + 3 + 5 + 7 + 13 + 21 + 35 + 39 + 65 + 91 + 195 + 273 + 455 + 1365 = 2568
How to Find Factors of 1365?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 1365. Identifying the numbers which are multiplied to get the number 1365 is the multiplication method.
Step 1: Multiply 1365 by 1, 1365 × 1 = 1365.
Step 2: Check for other numbers that give 1365 after multiplying
3 × 455 = 1365
5 × 273 = 1365
7 × 195 = 1365
13 × 105 = 1365
Therefore, the positive factor pairs of 1365 are: (1, 1365), (3, 455), (5, 273), (7, 195), (13, 105).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 1365 by 1, 1365 ÷ 1 = 1365.
Step 2: Continue dividing 1365 by the numbers until the remainder becomes 0.
1365 ÷ 1 = 1365
1365 ÷ 3 = 455
1365 ÷ 5 = 273
1365 ÷ 7 = 195
1365 ÷ 13 = 105
Therefore, the factors of 1365 are: 1, 3, 5, 7, 13, 21, 35, 39, 65, 91, 195, 273, 455, and 1365.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 1365 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1365 ÷ 3 = 455
455 ÷ 5 = 91
91 ÷ 7 = 13
13 ÷ 13 = 1
The prime factors of 1365 are 3, 5, 7, and 13.
The prime factorization of 1365 is: 3 × 5 × 7 × 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, 1365 is divided by 3 to get 455.
Step 2: Now divide 455 by 5 to get 91.
Step 3: Then divide 91 by 7 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1365 is: 3 × 5 × 7 × 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 1365: (1, 1365), (3, 455), (5, 273), (7, 195), and (13, 105).
Negative factor pairs of 1365: (-1, -1365), (-3, -455), (-5, -273), (-7, -195), and (-13, -105).
Common Mistakes and How to Avoid Them in Factors of 1365
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 1365, 1 and 1365 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 1365 include -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1365/1.5 = 910, 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 1365 are prime numbers.
For example, 3, 5, 7, and 13 are the prime factors of 1365, but it has other factors like 21, 35.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1365 as 3 × 5 × 7 × 13 and missing all the key factors.
Factors of 1365 Examples
Problem 1
There are 13 friends and 1365 candies. How will they divide it equally?
They will get 105 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
1365/13 = 105
Problem 2
A field is rectangular, the length of the field is 39 meters and the total area is 1365 square meters. Find the width?
35 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1365 = 39 × width
To find the value of width, we need to shift 39 to the left side.
1365/39 = width
Width = 35.
Problem 3
There are 21 bags and 1365 marbles. How many marbles will be in each bag?
Each bag will have 65 marbles.
Explanation
To find the marbles in each bag, divide the total marbles by the number of bags.
1365/21 = 65
Problem 4
In a class, there are 1365 students, and 65 groups. How many students are there in each group?
There are 21 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1365/65 = 21
Problem 5
1365 books need to be arranged in 273 shelves. How many books will go on each shelf?
Each of the shelves has 5 books.
Explanation
Divide total books by shelves.
1365/273 = 5
FAQs on Factors of 1365
1.What are the factors of 1365?
2.Mention the prime factors of 1365.
3.Is 1365 a multiple of 7?
4.Mention the factor pairs of 1365?
5.What is the square of 1365?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 1365?
7.What are some fun ways kids in United Kingdom can practice Factors of 1365 with numbers?
8.What role do numbers and Factors of 1365 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 1365 skills?
Important Glossaries for Factors of 1365
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1365 are 1, 3, 5, 7, 13, 21, 35, 39, 65, 91, 195, 273, 455, and 1365.
- Prime factors: The factors which are prime numbers. For example, 3, 5, 7, and 13 are prime factors of 1365.
- 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 1365 are (1, 1365), (3, 455), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1365 is 3 × 5 × 7 × 13.
- Negative factors: Factors that are negative numbers. For example, -1, -3, -5 are negative factors of 1365.
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About BrightChamps in United Kingdom
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.
