Greatest Common Factor of 585 and 588

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 585, 588 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 585 and 588 is 3.

GCF(585,588) = 3

GCF of 585 and 588

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 585 and 588

GCF of 585 and 588 is 3

Prime Factorization of 585


3 585
3 195
5 65
13 13
1

Prime factors of 585 are 3,5,13. Prime factorization of 585 in exponential form is:

585 = 32×51×131

Prime Factorization of 588


2 588
2 294
3 147
7 49
7 7
1

Prime factors of 588 are 2,3,7. Prime factorization of 588 in exponential form is:

588 = 22×31×72

∴ So by taking common prime factors GCF of 585 and 588 is 3

Greatest Common Factor of 585 and 588 by matching factors method

Factors of 585

List of positive integer factors of 585 that divides 585 without a remainder.

1,3,5,9,13,15,39,45,65,117,195,585

Factors of 588

List of positive integer factors of 588 that divides 588 without a remainder.

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

Greatest Common Factor

We found the factors and prime factorization of 585 and 588. The biggest common factor number is the GCF number.
So the greatest common factor 585 and 588 is 3.

Also check out the Least Common Multiple of 585 and 588

Properties of GCF 585 and 588

(i) The GCF of 585 and 588 is associative

GCF of 585 and 588 = GCF of 588 and 585

Related Greatest Common Factor of 585

Related Greatest Common Factor of 588

Frequently Asked Questions on GCF of 585 and 588

1. What is the GCF of 585 and 588?

Answer: GCF of 585 and 588 is 3.

2. What are the Factors of 585?

Answer: Factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585. There are 12 integers that are factors of 585. The greatest factor of 585 is 585.

3. What are the Factors of 588?

Answer: Factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588. There are 18 integers that are factors of 588. The greatest factor of 588 is 588.

4. How to Find the GCF of 585 and 588?

Answer:

Greatest Common Factor of 585 and 588 = 3

Step 1: Find the prime factorization of 585

585 = 3 x 3 x 5 x 13

Step 2: Find the prime factorization of 588

588 = 2 x 2 x 3 x 7 x 7

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 3

Step 4: Therefore, the greatest common factor of 585 and 588 is 3