261 LearnersLast updated on May 26th, 2025
Factors of 588
Factors of 588 are numbers that can divide 588 completely without the remainder. We often use factors like organizing events and seating arrangements in our daily lives. In this topic, we will know more about the factors of 588 and the different methods to find them.
What are the 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
|
Positive Factors |
Negative Factors |
Prime Factors |
Prime Factorization |
|
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 196, 294, 588 |
-1, -2, -3, -4, -6, -7, -8, -12, -14, -21, -24, -28, -42, -49, -56, -84, -98, -147, -196, -294, -588 |
2, 3, 7 |
22 × 31 × 72 |
|
Positive Factors |
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 196, 294, 588 |
|
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 |
2, 3, 7 |
| Prime Factorization | 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.
How to Find the Factors of 588?
There are different methods to find the factors of 588.
Methods to find the factors of 588:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
Finding Factors Using Multiplication Method
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.
Finding Factors Using Division Method
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.
Prime Factors and Prime Factorization
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
Factor Tree
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)
Common Mistakes and How to Avoid Them in Factors of 588
Mistakes are those steps that help us to understand more about something. Learn about the common errors that can occur. Solutions to solve the common mistakes are given below.
Mistake 1
Assuming a number like 49 as a non-factor.
When 49 is multiplied by 12 (49 × 12), we get 588 as the product. Hence, 49 is a factor of 588. Kids can find it difficult to understand that bigger numbers like 49 can exist as a factor. Always remember that factors are whole numbers that will divide the given number completely.
Solved Examples for Factors of 588
Problem 1
Can you check whether 24 and 42 are co-prime?
No, 24 and 42 are not co-primes.
Explanation
To check whether two numbers are co-prime, list their factors first. Once you have listed the factors, identify the common factors and determine the GCF. If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Here, the GCF is 6. So 24 and 42 are not co-prime. For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 588 is a multiple of 7
Yes, 588 is a multiple of 7.
Explanation
Multiples of 7 are numbers we get when 7 is multiplied by another number. 588 ÷ 7 = 84, which is an integer, confirming that 588 is a multiple of 7.
Problem 3
Identify the perfect square from the factors of 588.
The perfect square factor of 588 is 36 and the root is 6.
Explanation
A perfect square is a number we get when the same number is multiplied twice. When 6 is multiplied twice (6 × 6), we get the perfect square 36.
Problem 4
What is the greatest common factor (GCF) of 588 and 72?
The GCF of 588 and 72 is 12.
Explanation
To find the GCF, list the factors of each number and identify the largest common factor.
Factors of 588: 1, 2, 3, 4, 6, 7, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 196, 294, 588
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The largest common factor is 12.
Problem 5
List all the factors of 588
The factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 196, 294, and 588.
Explanation
The numbers that do not leave any remainder when divided by 588 are the factors of 588.
FAQ’s for Factors of 588.
1.What are the factors of 588?
2.How do you determine if a number is a factor of 588?
3.What is the smallest factor of 588?
4.What is the largest factor of 588?
5.How many factors does 588 have?
6.How many odd factors does 588 have?
7.What factors go into 588?
8.Do any perfect squares exist in the factors of 588?
Glossaries for Factors of 588.
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.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
