127 LearnersLast updated on May 26th, 2025
Factors of 585
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.
What are the Factors of 585?
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
How to Find Factors of 585?
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 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.
Finding Factors Using Division Method
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.
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 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).
Factor Tree
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).
Common Mistakes and How to Avoid Them in Factors of 585
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 integer. Always remember to include 1 and the number itself.
For example, in factors of 585, 1 and 585 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 585 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes mistakenly include fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 585/1.5 = 390, 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 585 are prime numbers.
For example, 3, 5, and 13 are the prime factors of 585, but it has other factors like 9, 45.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 585 as \(3^2 \times 5 \times 13\) and missing all the key factors.
Factors of 585 Examples
Problem 1
There are 9 boxes and 585 marbles. How will the marbles be divided equally?
They will get 65 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of boxes.
585/9 = 65
Problem 2
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.
Explanation
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.
Problem 3
There are 39 tables and 585 chairs. How many chairs will be at each table?
Each table will have 15 chairs.
Explanation
To find the chairs at each table, divide the total chairs by the number of tables.
585/39 = 15
Problem 4
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.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
585/15 = 39
Problem 5
585 books need to be arranged in 13 shelves. How many books will go on each shelf?
Each of the shelves has 45 books.
Explanation
Divide total books by shelves.
585/13 = 45
FAQs on Factors of 585
1.What are the factors of 585?
2.Mention the prime factors of 585.
3.Is 585 a multiple of 9?
4.Mention the factor pairs of 585?
5.What is the square of 585?
Important Glossaries for Factors of 585
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, and 585.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 13 are prime factors of 585.
- 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 585 are (1, 585), (3, 195), etc.
- Prime factorization: The expression of a number as a product of its prime factors, like (32 times 5 times 13) for 585.
- Negative factors: Factors that are negative counterparts of positive factors. For example, -1, -3, -5, etc., are negative factors of 585.
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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.
