138 LearnersLast updated on May 30th, 2025
Factors of 1605
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 1605, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1605?
The numbers that divide 1605 evenly are known as factors of 1605.
A factor of 1605 is a number that divides the number without remainder.
The factors of 1605 are 1, 3, 5, 15, 107, 321, 535, and 1605.
Negative factors of 1605: -1, -3, -5, -15, -107, -321, -535, and -1605.
Prime factors of 1605: 3, 5, and 107.
Prime factorization of 1605: 3 × 5 × 107. The sum of factors of 1605: 1 + 3 + 5 + 15 + 107 + 321 + 535 + 1605 = 2592
How to Find Factors of 1605?
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 1605. Identifying the numbers which are multiplied to get the number 1605 is the multiplication method.
Step 1: Multiply 1605 by 1, 1605 × 1 = 1605.
Step 2: Check for other numbers that give 1605 after multiplying
3 × 535 = 1605
5 × 321 = 1605
15 × 107 = 1605
Therefore, the positive factor pairs of 1605 are: (1, 1605), (3, 535), (5, 321), (15, 107).
All these factor pairs result in 1605. 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 1605 by 1, 1605 ÷ 1 = 1605.
Step 2: Continue dividing 1605 by the numbers until the remainder becomes 0.
1605 ÷ 1 = 1605
1605 ÷ 3 = 535
1605 ÷ 5 = 321
1605 ÷ 15 = 107
Therefore, the factors of 1605 are: 1, 3, 5, 15, 107, 321, 535, 1605.
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 1605 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1605 ÷ 3 = 535
535 ÷ 5 = 107
107 ÷ 107 = 1
The prime factors of 1605 are 3, 5, and 107.
The prime factorization of 1605 is: 3 × 5 × 107.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1605 is divided by 3 to get 535.
Step 2: Now divide 535 by 5 to get 107.
Step 3: Then divide 107 by 107 to get 1.
Here, 107 is a prime number and cannot be divided anymore.
So, the prime factorization of 1605 is: 3 × 5 × 107.
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 1605: (1, 1605), (3, 535), (5, 321), and (15, 107).
Negative factor pairs of 1605: (-1, -1605), (-3, -535), (-5, -321), and (-15, -107).
Common Mistakes and How to Avoid Them in Factors of 1605
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 1605, 1 and 1605 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1605 consist of -1, -3, -5, etc.
Mistake 3
Including Fractions
Children might sometimes mistakenly add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1605/1.5 ≈ 1070, 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 1605 are prime numbers.
For example, 3, 5, and 107 are the prime factors of 1605, but it has other factors like 15, 321.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1605 as 3 × 5 × 107 and missing all the key factors.
Factors of 1605 Examples
Problem 1
There are 3 teams and 1605 participants in a sports event. How will they divide the participants equally?
They will have 535 participants in each team.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
1605/3 = 535
Problem 2
A concert hall has 5 sections and can accommodate a total of 1605 people. How many people can each section hold?
Each section can hold 321 people.
Explanation
To find the number of people in each section, we use the formula,
Total people = sections × people per section
1605 = 5 × people per section
To find the value of people per section, divide 1605 by 5.
1605/5 = 321
Problem 3
There are 15 buses and 1605 students. How many students will be in each bus?
Each bus will have 107 students.
Explanation
To find the students in each bus, divide the total students by the buses.
1605/15 = 107
Problem 4
In a library, there are 1605 books, and they need to be arranged in 5 shelves. How many books will go on each shelf?
Each shelf will have 321 books.
Explanation
Divide the total books by the shelves.
1605/5 = 321
Problem 5
A company has 107 employees and plans to divide them into 3 teams. How many employees will be in each team?
There will be 535 employees in each team.
Explanation
Divide the total number of employees by the number of teams.
1605/3 = 535
FAQs on Factors of 1605
1.What are the factors of 1605?
2.Mention the prime factors of 1605.
3.Is 1605 a multiple of 5?
4.Mention the factor pairs of 1605?
5.What is the square of 1605?
Important Glossaries for Factors of 1605
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1605 are 1, 3, 5, 15, 107, 321, 535, and 1605.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 107 are prime factors of 1605.
- 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 1605 are (1, 1605), (3, 535), etc.
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 1605 is 3 × 5 × 107.
- Multiple: A number that can be divided by another number without a remainder. For example, 1605 is a multiple of 5.
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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.
