Factors of 588

The factors of 588 are the numbers that divide 588 evenly.

Positive Factors: These are the positive numbers that divide 588 evenly.
The factors of 588 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 196, 294, and 588.
 

Negative Factors: These are negative counterparts of the positive factors.
Negative factors: -1, -2, -3, -4, -6, -7, -8, -12, -14, -21, -24, -28, -42, -49, -56, -84, -98, -147, -196, -294, -588
 

Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 588 as the product.
Prime factors: 2, 3, 7
 

Prime Factorization: Prime factorization involves breaking 588 into its prime factors
It is expressed as 2² × 3¹ × 7²

This breakdown helps in understanding the various factors of 588, whether they are positive or negative, as well as how prime factorization works for this number.

There are different methods to find the factors of 588.

Methods to find the factors of 588:

1. Multiplication Method
2. Division Method
3. Prime Factor and Prime Factorization
4. Factor Tree
    

The multiplication method finds the pair of factors that give 588 as their product.
 

Step 1: Find the pair of numbers whose product is 588.
 

Step 2: The factors are those numbers, when multiplied, give 588.
 

Step 3: Make a list of numbers whose product will be 588.
A list of numbers whose products are 588 is given below:
1 × 588 = 588
2 × 294 = 588
3 × 196 = 588
4 × 147 = 588
6 × 98 = 588
7 × 84 = 588
12 × 49 = 588
14 × 42 = 588
21 × 28 = 588

Thus, the factors of 588 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 196, 294, and 588.
 

The division method finds the numbers that fully divide the given number. The steps are given below:
 

Step 1: Since every number is divisible by 1, 1 will always be a factor. Example: 588 ÷ 1 = 588
 

Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.

Thus, the factors of 588 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 196, 294, and 588.
 

Multiplying prime numbers to get the given number as their product is called prime factors. A number when it is simplified using the factors of that number and is expressed in the form of prime factors is the prime factorization of a number.

Prime Factors of 588: Number 588 has three prime factors.
Prime factors of 588: 2, 3, 7

To find the prime factors of 588, we can divide 588 with the prime numbers 2, 3, and 7 from the list of factors of 588.
Step 1: Divide 588 with the prime number 2
588 ÷ 2 = 294
 

Step 2: Divide 294 with the prime number 2
294 ÷ 2 = 147
 

Step 3: Divide 147 with the prime number 3
147 ÷ 3 = 49
 

Step 4: Divide 49 with the prime number 7
49 ÷ 7 = 7
 

Step 5: Divide 7 with the prime number 7
7 ÷ 7 = 1
 

Prime Factorization of 588: Prime factorization breaks down the prime factors of 588.
Expressed as 2² × 3¹ × 7²

The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.

This tree shows the breakdown of 588 into its prime factors: 2 × 3 × 7.

Positive and Negative Factor Pairs of 588
Factors of 588 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.
 

Positive Factor Pairs: (1, 588), (2, 294), (3, 196), (4, 147), (6, 98), (7, 84), (12, 49), (14, 42), (21, 28)
 

Negative Factor Pairs: (-1, -588), (-2, -294), (-3, -196), (-4, -147), (-6, -98), (-7, -84), (-12, -49), (-14, -42), (-21, -28)
 

Factors: Numbers that can divide a given number completely without leaving a remainder.
 

Prime Factorization: The process of breaking down a number into its prime factors and expressing it as a product of prime numbers.
 

Prime Factors: Prime numbers that, when multiplied together, give the original number.
 

Factor Tree: A visual tool used to break down a number into its prime factors, where each branch represents a factorization step.