# Factors of 588

Factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, and 588

#### How to find factors of a number

 1.   Find factors of 588 using Division Method 2.   Find factors of 588 using Prime Factorization 3.   Find factors of 588 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 588

• Divide 588 by 1: 588 ÷ 1 : Remainder = 0
• Divide 588 by 2: 588 ÷ 2 : Remainder = 0
• Divide 588 by 3: 588 ÷ 3 : Remainder = 0
• Divide 588 by 4: 588 ÷ 4 : Remainder = 0
• Divide 588 by 6: 588 ÷ 6 : Remainder = 0
• Divide 588 by 7: 588 ÷ 7 : Remainder = 0
• Divide 588 by 12: 588 ÷ 12 : Remainder = 0
• Divide 588 by 14: 588 ÷ 14 : Remainder = 0
• Divide 588 by 21: 588 ÷ 21 : Remainder = 0
• Divide 588 by 28: 588 ÷ 28 : Remainder = 0
• Divide 588 by 42: 588 ÷ 42 : Remainder = 0
• Divide 588 by 49: 588 ÷ 49 : Remainder = 0
• Divide 588 by 84: 588 ÷ 84 : Remainder = 0
• Divide 588 by 98: 588 ÷ 98 : Remainder = 0
• Divide 588 by 147: 588 ÷ 147 : Remainder = 0
• Divide 588 by 196: 588 ÷ 196 : Remainder = 0
• Divide 588 by 294: 588 ÷ 294 : Remainder = 0
• Divide 588 by 588: 588 ÷ 588 : Remainder = 0

Hence, Factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, and 588

#### 2. Steps to find factors of 588 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 588 using the division method, follow these steps:

• Step 1. Start dividing 588 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 588, which is 2. Divide 588 by 2 to obtain the quotient (294).
588 ÷ 2 = 294
• Step 3. Repeat step 1 with the obtained quotient (294).
294 ÷ 2 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 588 is, 588 = 2 x 2 x 3 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 588 as shown below:

So, the prime factorization of 588 is, 588 = 2 x 2 x 3 x 7 x 7.

#### 3. Find factors of 588 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 588 would be the two numbers which, when multiplied, give 588 as the result.

The following table represents the calculation of factors of 588 in pairs:

Factor Pair Pair Factorization
1 and 588 1 x 588 = 588
2 and 294 2 x 294 = 588
3 and 196 3 x 196 = 588
4 and 147 4 x 147 = 588
6 and 98 6 x 98 = 588
7 and 84 7 x 84 = 588
12 and 49 12 x 49 = 588
14 and 42 14 x 42 = 588
21 and 28 21 x 28 = 588

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 588. They are called negative pair factors.

Hence, the negative pairs of 588 would be ( -1 , -588 ) , ( -2 , -294 ) , ( -3 , -196 ) , ( -4 , -147 ) , ( -6 , -98 ) , ( -7 , -84 ) , ( -12 , -49 ) , ( -14 , -42 ) and ( -21 , -28 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 588 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 588.
• Every number is a factor of zero (0), since 588 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588 are exact divisors of 588.
• Factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588. Each factor divides 588 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588 are all less than or equal to 588.

• What are the prime factors of 588?

The factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588.
Prime factors of 588 are 2, 2, 3, 7, 7.

• What two numbers make 588?

Two numbers that make 588 are 2 and 294.

• What is the greatest prime factors of 588?

The greatest prime factor of 588 is 7.

• What are factors of 588?

Factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588.

• How do you find factors of a negative number? ( eg. -588 )?

Factors of -588 are -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42, -49, -84, -98, -147, -196, -294, -588.

• What are five multiples of 588?

First five multiples of 588 are 1176, 1764, 2352, 2940, 3528.

• Write some multiples of 588?

First five multiples of 588 are 1176, 1764, 2352, 2940.

• Is 588 a perfect square?

No 588 is not a perfect square.

• What two numbers make 588?

Two numbers that make 588 are 2 and 294.

#### Examples of Factors

What is prime factorization of 588?

Prime factorization of 588 is 2 x 2 x 3 x 7 x 7 = 22 x 3 x 72.

Sammy is puzzled while calculating the prime factors of 588. Can you help him find them?

Factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588.
Prime factors of 588 are 2, 2, 3, 7, 7

Kevin has been asked to write 17 factor(s) of 588. Can you predict the answer?

17 factor(s) of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294.

Joey wants to write all the prime factors of 588 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 588 are 2, 2, 3, 7, 7.
So in exponential form it can be written as 22 x 3 x 72.

How many factors are there for 588?

Factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588.
So there are in total 18 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 588? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588.
Negative factors are -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42, -49, -84, -98, -147, -196, -294, -588.

Can you help Rubel to find out the product of the even factors of 588?

Factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588.
Even factors of 588 are 2, 4, 6, 12, 14, 28, 42, 84, 98, 196, 294, 588.
Hence, product of even factors of 588 is; 2 x 4 x 6 x 12 x 14 x 28 x 42 x 84 x 98 x 196 x 294 x 588 = 2645111175781810000.