# Factors of 589

Factors of 589 are 1, 19, 31, and 589

#### How to find factors of a number

 1.   Find factors of 589 using Division Method 2.   Find factors of 589 using Prime Factorization 3.   Find factors of 589 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 589

• Divide 589 by 1: 589 ÷ 1 : Remainder = 0
• Divide 589 by 19: 589 ÷ 19 : Remainder = 0
• Divide 589 by 31: 589 ÷ 31 : Remainder = 0
• Divide 589 by 589: 589 ÷ 589 : Remainder = 0

Hence, Factors of 589 are 1, 19, 31, and 589

#### 2. Steps to find factors of 589 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 589 using the division method, follow these steps:

• Step 1. Start dividing 589 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 589, which is 19. Divide 589 by 19 to obtain the quotient (31).
589 ÷ 19 = 31
• Step 3. Repeat step 1 with the obtained quotient (31).
31 ÷ 31 = 1

So, the prime factorization of 589 is, 589 = 19 x 31.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 589 as shown below:

So, the prime factorization of 589 is, 589 = 19 x 31.

#### 3. Find factors of 589 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 589 would be the two numbers which, when multiplied, give 589 as the result.

The following table represents the calculation of factors of 589 in pairs:

Factor Pair Pair Factorization
1 and 589 1 x 589 = 589
19 and 31 19 x 31 = 589

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 589. They are called negative pair factors.

Hence, the negative pairs of 589 would be ( -1 , -589 ) , ( -19 , -31 ) .

#### How can we define factors?

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

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 19, 31, 589 are exact divisors of 589.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 589 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 589.

• Is 589 a perfect square?

No 589 is not a perfect square.

• What are factors of 589?

Factors of 589 are 1, 19, 31, 589.

• Which is greatest factor of 589?

The greatest factor of 589 is 31.

• What is the sum of all factors of 589?

The sum of all factors of 589 is 640.

• What are multiples of 589?

First five multiples of 589 are 1178, 1767, 2356, 2945.

• What is the greatest prime factors of 589?

The greatest prime factor of 589 is 31.

• What are six multiples of 589?

First five multiples of 589 are 1178, 1767, 2356, 2945, 3534, 4123.

• What is prime factorization of 589?

Prime factorization of 589 is 19 x 31.

• Is 589 a whole number?

Yes 589 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 589? Help her in writing all the factors.

Positive factors are 1, 19, 31, 589.
Negative factors are -1, -19, -31, -589.

Can you help Sammy find out the product of the odd factors of 589?

Factors of 589 are 1, 19, 31, 589.
Odd factors of 589 are 1, 19, 31, 589.
Hence product of odd factors of 589 is; 1 x 19 x 31 x 589 = 346921.

Joey wants to write all the prime factors of 589 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 589 are 19, 31.
So in exponential form it can be written as 19 x 31.

How many factors are there for 589?

Factors of 589 are 1, 19, 31, 589.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 589. Can you predict the answer?

3 factor(s) of 589 are 1, 19, 31.

Sammy is puzzled while calculating the prime factors of 589. Can you help him find them?

Factors of 589 are 1, 19, 31, 589.
Prime factors of 589 are 19, 31

What is prime factorization of 589?

Prime factorization of 589 is 19 x 31 = 19 x 31.