Last updated on May 26th, 2025
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 585, how they are used in real life, and tips to learn them quickly.
The numbers that divide 585 evenly are known as factors of 585.
A factor of 585 is a number that divides the number without remainder.
The factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, and 585.
Negative factors of 585: -1, -3, -5, -9, -13, -15, -39, -45, -65, -117, -195, and -585.
Prime factors of 585: 3, 5, and 13.
Prime factorization of 585: 3 × 3 × 5 × 13 or \(32 times 5 times 13).
The sum of factors of 585: 1 + 3 + 5 + 9 + 13 + 15 + 39 + 45 + 65 + 117 + 195 + 585 = 1092
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 585. Identifying the numbers which are multiplied to get the number 585 is the multiplication method.
Step 1: Multiply 585 by 1, 585 × 1 = 585.
Step 2: Check for other numbers that give 585 after multiplying
3 × 195 = 585
5 × 117 = 585
9 × 65 = 585
13 × 45 = 585
15 × 39 = 585
Therefore, the positive factor pairs of 585 are: (1, 585), (3, 195), (5, 117), (9, 65), (13, 45), and (15, 39). For every positive factor, there is a negative factor.
Dividing the given number 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 the simple division method -
Step 1: Divide 585 by 1, 585 ÷ 1 = 585.
Step 2: Continue dividing 585 by the numbers until the remainder becomes 0.
585 ÷ 1 = 585
585 ÷ 3 = 195
585 ÷ 5 = 117
585 ÷ 9 = 65
585 ÷ 13 = 45
585 ÷ 15 = 39
Therefore, the factors of 585 are: 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, and 585.
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 585 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
585 ÷ 3 = 195
195 ÷ 3 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
The prime factors of 585 are 3, 5, and 13.
The prime factorization of 585 is: (32 times 5 times 13).
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 585 is divided by 3 to get 195.
Step 2: Now divide 195 by 3 to get 65.
Step 3: Then divide 65 by 5 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 585 is: (32 times 5 times 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 585: (1, 585), (3, 195), (5, 117), (9, 65), (13, 45), and (15, 39).
Negative factor pairs of 585: (-1, -585), (-3, -195), (-5, -117), (-9, -65), (-13, -45), and (-15, -39).
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 9 boxes and 585 marbles. How will the marbles be divided equally?
They will get 65 marbles each.
To divide the marbles equally, we need to divide the total marbles by the number of boxes.
585/9 = 65
A garden is rectangular, the length of the garden is 13 meters, and the total area is 585 square meters. Find the width.
45 meters.
To find the width of the garden, we use the formula,
Area = length × width
585 = 13 × width
To find the value of width, we need to shift 13 to the left side.
585/13 = width
Width = 45.
There are 39 tables and 585 chairs. How many chairs will be at each table?
Each table will have 15 chairs.
To find the chairs at each table, divide the total chairs by the number of tables.
585/39 = 15
In a class, there are 585 students, and 15 groups. How many students are there in each group?
There are 39 students in each group.
Dividing the students by the total groups, we will get the number of students in each group.
585/15 = 39
585 books need to be arranged in 13 shelves. How many books will go on each shelf?
Each of the shelves has 45 books.
Divide total books by shelves.
585/13 = 45
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.