Last updated on May 30th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To divide the participants equally, we need to divide the total participants by the number of teams.
1605/3 = 535
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.
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
There are 15 buses and 1605 students. How many students will be in each bus?
Each bus will have 107 students.
To find the students in each bus, divide the total students by the buses.
1605/15 = 107
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.
Divide the total books by the shelves.
1605/5 = 321
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.
Divide the total number of employees by the number of teams.
1605/3 = 535
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.
: She loves to read number jokes and games.