# Factors of 585

Factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, and 585

#### How to find factors of a number

 1.   Find factors of 585 using Division Method 2.   Find factors of 585 using Prime Factorization 3.   Find factors of 585 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 585

• Divide 585 by 1: 585 ÷ 1 : Remainder = 0
• Divide 585 by 3: 585 ÷ 3 : Remainder = 0
• Divide 585 by 5: 585 ÷ 5 : Remainder = 0
• Divide 585 by 9: 585 ÷ 9 : Remainder = 0
• Divide 585 by 13: 585 ÷ 13 : Remainder = 0
• Divide 585 by 15: 585 ÷ 15 : Remainder = 0
• Divide 585 by 39: 585 ÷ 39 : Remainder = 0
• Divide 585 by 45: 585 ÷ 45 : Remainder = 0
• Divide 585 by 65: 585 ÷ 65 : Remainder = 0
• Divide 585 by 117: 585 ÷ 117 : Remainder = 0
• Divide 585 by 195: 585 ÷ 195 : Remainder = 0
• Divide 585 by 585: 585 ÷ 585 : Remainder = 0

Hence, Factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, and 585

#### 2. Steps to find factors of 585 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 585 using the division method, follow these steps:

• Step 1. Start dividing 585 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 585, which is 3. Divide 585 by 3 to obtain the quotient (195).
585 ÷ 3 = 195
• Step 3. Repeat step 1 with the obtained quotient (195).
195 ÷ 3 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1

So, the prime factorization of 585 is, 585 = 3 x 3 x 5 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 585 as shown below:

So, the prime factorization of 585 is, 585 = 3 x 3 x 5 x 13.

#### 3. Find factors of 585 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 585 would be the two numbers which, when multiplied, give 585 as the result.

The following table represents the calculation of factors of 585 in pairs:

Factor Pair Pair Factorization
1 and 585 1 x 585 = 585
3 and 195 3 x 195 = 585
5 and 117 5 x 117 = 585
9 and 65 9 x 65 = 585
13 and 45 13 x 45 = 585
15 and 39 15 x 39 = 585

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 585. They are called negative pair factors.

Hence, the negative pairs of 585 would be ( -1 , -585 ) , ( -3 , -195 ) , ( -5 , -117 ) , ( -9 , -65 ) , ( -13 , -45 ) and ( -15 , -39 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585 are exact divisors of 585.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 585 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 585.

• Which is the smallest prime factor of 585?

Smallest prime factor of 585 is 3.

• Is 585 a perfect square?

No 585 is not a perfect square.

• What are five multiples of 585?

First five multiples of 585 are 1170, 1755, 2340, 2925, 3510.

• What is prime factorization of 585?

Prime factorization of 585 is 3 x 3 x 5 x 13.

• What are factors of 585?

Factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585.

• How do you find factors of a negative number? ( eg. -585 )?

Factors of -585 are -1, -3, -5, -9, -13, -15, -39, -45, -65, -117, -195, -585.

• Is 585 a whole number?

Yes 585 is a whole number.

• Which is greatest factor of 585?

The greatest factor of 585 is 195.

• What are the prime factors of 585?

The factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585.
Prime factors of 585 are 3, 3, 5, 13.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 585. Can you help her?

Prime factors of 585 are 3, 3, 5, 13.
Hence, the product of prime factors of 195.

Can you help Rubel to find out the product of the even factors of 585?

Factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585.
Even factors of 585 are 0.
Hence, product of even factors of 585 is; 0 = 0.

Joy wants to calculate mean of all the factors of 585. Help him in finding the mean of 585.

Factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 585 is 1 + 3 + 5 + 9 + 13 + 15 + 39 + 45 + 65 + 117 + 195 + 585 = 1092.
Hence, the mean of factors of 585 is 1092 ÷ 12 = 91.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 585? Help her in writing all the factors.

Positive factors are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585.
Negative factors are -1, -3, -5, -9, -13, -15, -39, -45, -65, -117, -195, -585.

How many factors are there for 585?

Factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585.
So there are in total 12 factors.

Joey wants to write all the prime factors of 585 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 585 are 3, 3, 5, 13.
So in exponential form it can be written as 32 x 5 x 13.

Kevin has been asked to write 11 factor(s) of 585. Can you predict the answer?

11 factor(s) of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195.