100 LearnersLast updated on May 26th, 2025
Factors of 1095
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 1095, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1095?
The numbers that divide 1095 evenly are known as factors of 1095.
A factor of 1095 is a number that divides the number without remainder.
The factors of 1095 are 1, 3, 5, 7, 15, 21, 35, 73, 105, 219, 365, and 1095.
Negative factors of 1095: -1, -3, -5, -7, -15, -21, -35, -73, -105, -219, -365, and -1095.
Prime factors of 1095: 3, 5, 7, and 73.
Prime factorization of 1095: 3 × 5 × 7 × 73.
The sum of factors of 1095: 1 + 3 + 5 + 7 + 15 + 21 + 35 + 73 + 105 + 219 + 365 + 1095 = 1944
How to Find Factors of 1095?
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 1095. Identifying the numbers which are multiplied to get the number 1095 is the multiplication method.
Step 1: Multiply 1095 by 1, 1095 × 1 = 1095.
Step 2: Check for other numbers that give 1095 after multiplying
3 × 365 = 1095
5 × 219 = 1095
7 × 157 = 1095
15 × 73 = 1095
Therefore, the positive factor pairs of 1095 are: (1, 1095), (3, 365), (5, 219), (7, 157), (15, 73).
All these factor pairs result in 1095.
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 1095 by 1, 1095 ÷ 1 = 1095.
Step 2: Continue dividing 1095 by the numbers until the remainder becomes 0.
1095 ÷ 1 = 1095
1095 ÷ 3 = 365
1095 ÷ 5 = 219
1095 ÷ 7 = 157
1095 ÷ 15 = 73
Therefore, the factors of 1095 are: 1, 3, 5, 7, 15, 21, 35, 73, 105, 219, 365, 1095.
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 1095 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1095 ÷ 3 = 365
365 ÷ 5 = 73
73 ÷ 73 = 1
The prime factors of 1095 are 3, 5, 7, and 73.
The prime factorization of 1095 is: 3 × 5 × 7 × 73.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1095 is divided by 3 to get 365.
Step 2: Now divide 365 by 5 to get 73.
Step 3: 73 is a prime number and cannot be divided further.
So, the prime factorization of 1095 is: 3 × 5 × 7 × 73.
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 1095: (1, 1095), (3, 365), (5, 219), (7, 157), (15, 73).
Negative factor pairs of 1095: (-1, -1095), (-3, -365), (-5, -219), (-7, -157), (-15, -73).
Common Mistakes and How to Avoid Them in Factors of 1095
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 1095, 1 and 1095 are also factors.
Factors of 1095 Examples
Problem 1
A charity has 1095 gift bags to distribute among 15 schools. How many gift bags will each school receive?
Each school will receive 73 gift bags.
Explanation
To distribute the gift bags equally, divide the total bags by the number of schools.
1095/15 = 73
Problem 2
A rectangular garden has a width of 21 meters and a total area of 1095 square meters. Find the length of the garden.
52.14 meters.
Explanation
To find the length of the garden, use the formula,
Area = length × width
1095 = length × 21
To find the value of length, divide both sides by 21.
1095/21 ≈ 52.14
Problem 3
A library has 365 books to be divided among 5 shelves. How many books will go on each shelf?
Each shelf will have 73 books.
Explanation
To find the books on each shelf, divide the total books by the number of shelves.
365/5 = 73
Problem 4
There are 219 students and 7 classes. How many students are there in each class?
There are 31 students in each class.
Explanation
Dividing the students by the total classes, we get the number of students in each class.
219/7 = 31
Problem 5
A company needs to distribute 1095 pens among 3 branches. How many pens will each branch receive?
Each branch will receive 365 pens.
Explanation
Divide the total pens by the number of branches.
1095/3 = 365
FAQs on Factors of 1095
1.What are the factors of 1095?
2.Mention the prime factors of 1095.
3.Is 1095 a multiple of 5?
4.Mention the factor pairs of 1095.
5.What is the sum of the factors of 1095?
6.How can children in Australia use numbers in everyday life to understand Factors of 1095?
7.What are some fun ways kids in Australia can practice Factors of 1095 with numbers?
8.What role do numbers and Factors of 1095 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 1095 skills?
Important Glossaries for Factors of 1095
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1095 are 1, 3, 5, 7, etc.
- Prime factors: The factors which are prime numbers. For example, 3, 5, 7, and 73 are prime factors of 1095.
- 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 1095 are (1, 1095), (3, 365), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number.
- Prime factorization: The process of breaking down a number into its basic prime factors. For example, the prime factorization of 1095 is 3 × 5 × 7 × 73.
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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
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