Factors of 588: Prime Factorization, Methods, and Examples

Numbers that divide the given number 588 perfectly are known as the 588 factors. The component of the number is its factor. 

If the given number is obtained by multiplying two-factor integers, then the factors of the number 588 can be either positive or negative.

Factors of 588

Here are the factors of number 588.

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

Negative Factors of 588

The negative factors of 588 are similar to their positive aspects, just with a negative sign.

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

Prime Factorization of 588

The prime factorization of 588 is the way of expressing its prime factors in the product form.

Prime Factorization: 2² x 3¹ x 7²

In this article, we will learn about the factors of 588 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the 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 and 588. These numbers are the factors as they do not leave any remainder when divided by 588.

The factors of 588 are classified as prime numbers and composite numbers. The prime factors of the number 588 can be determined using the prime factorization technique.

How To Find the Factors of 588?

You can find the factors of 588 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 588, create a list containing the numbers that are exactly divisible by 588 with zero remainders. One important thing to note is that 1 and588  are the 588’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 588 are determined as follows:

\[\dfrac{588}{1} = 588\]

\[\dfrac{588}{2} = 294\]

\[\dfrac{588}{3} = 196\]

\[\dfrac{588}{4} = 147\]

\[\dfrac{588}{6} = 98\]

\[\dfrac{588}{7} = 84\]

\[\dfrac{588}{12} = 49\]

\[\dfrac{588}{14} = 42\]

\[\dfrac{588}{21} = 28\]

\[\dfrac{588}{28} = 21\]

\[\dfrac{588}{42} =14\]

\[\dfrac{588}{49} = 12\]

\[\dfrac{588}{84} = 7\]

\[\dfrac{588}{98} = 6\]

\[\dfrac{588}{147} = 4\]

\[\dfrac{588}{196} = 3\]

\[\dfrac{588}{294} = 2\]

\[\dfrac{588}{588} = 1\]

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

Total Number of Factors of 588

For 588, there are 18 positive factors and 18 negative ones. So in total, there are 36 factors of 588. 

To find the total number of factors of the given number, follow the procedure mentioned below:

1. Find the factorization/prime factorization of the given number.
2. Demonstrate the prime factorization of the number in the form of exponent form.
3. Add 1 to each of the exponents of the prime factor.
4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 588 is given as:

Factorization of 588 is 2² x 3¹ x 7².

The exponent of 2 is 2, 3 is 1, and 7 is 2.

Adding 1 to each and multiplying them together results in 36.

Therefore, the total number of factors of 588 is 36. 18 are positive, and 18 factors are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

• The factor of any given number must be a whole number.
• The factors of the number cannot be in the form of decimals or fractions.
• Factors can be positive as well as negative.
• Negative factors are the additive inverse of the positive factors of a given number.
• The factor of a number cannot be greater than that number.
• Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 588 by Prime Factorization

The number 588 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of588 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 588, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 588 can be expressed as:

588 = 2² x 3¹ x 7²

Factors of 588 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.

For 588, the factor pairs can be found as:

1 x 588 = 588

2 x 294 = 588

3 x 196 = 588

4 x 147 = 588

6 x 98 = 588

7 x 84 = 588

12 x 49 = 588

14 x 42 = 588

21 x 28 = 588

The possible factor pairs of 588 are given as (1, 588),(2, 294),(3, 196),(4, 147),(6, 98),(7, 84),(12, 49),(14, 42) and (21, 28).

All these numbers in pairs, when multiplied, give 588 as the product.

The negative factor pairs of 588 are given as:

-1 x -588 = 588

-2 x -294 = 588

-3 x -196 = 588

-4 x -147 = 588

-6 x -98 = 588

-7 x -84 = 588

-12 x -49 = 588

-14 x- 42 = 588

-21 x -28 = 588

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42, -49, -84, -98, -147, -196, -294 and -588 are called negative factors of 588.

The list of all the factors of 588, including positive as well as negative numbers, is given below.

Factor list of 588:1, -1,2, -2,3,-3, 4,-4, 6,-6, 7,-7, 12,-12, 14,-14,21,-21, 28,-28,42, -42, 49,-49, 84,-84, 98,-98, 147,-147, 196,-196, 294,-294, 588, and -588

Factors of 588 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 588 are there?

Solution

The total number of Factors of 588 is 36.

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

Example 2

Find the factors of 588 using prime factorization.

Solution

The prime factorization of 588 is given as:

588 $\div$ 2 = 294

294 $\div$ 2 =147 

147 $\div$ 3 = 49

49 $\div$ 7 = 7 

7 $\div$ 7 = 1 

So the prime factorization of 588 can be written as:

2² x 3¹ x 7² = 588

Factors of 587|Factors List| Factors of 589