Greatest Common Factor of 578 and 584

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 578, 584 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 578 and 584 is 2.

GCF(578,584) = 2

GCF of 578 and 584

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

GCF of:
and

Greatest Common Factor of 578 and 584

GCF of 578 and 584 is 2

Prime Factorization of 578


2 578
17 289
17 17
1

Prime factors of 578 are 2,17. Prime factorization of 578 in exponential form is:

578 = 21×172

Prime Factorization of 584


2 584
2 292
2 146
73 73
1

Prime factors of 584 are 2,73. Prime factorization of 584 in exponential form is:

584 = 23×731

∴ So by taking common prime factors GCF of 578 and 584 is 2

Greatest Common Factor of 578 and 584 by matching factors method

Factors of 578

List of positive integer factors of 578 that divides 578 without a remainder.

1,2,17,34,289,578

Factors of 584

List of positive integer factors of 584 that divides 584 without a remainder.

1,2,4,8,73,146,292,584

Greatest Common Factor

We found the factors and prime factorization of 578 and 584. The biggest common factor number is the GCF number.
So the greatest common factor 578 and 584 is 2.

Also check out the Least Common Multiple of 578 and 584

Properties of GCF 578 and 584

(i) The GCF of 578 and 584 is associative

GCF of 578 and 584 = GCF of 584 and 578

Related Greatest Common Factor of 578

Related Greatest Common Factor of 584

Frequently Asked Questions on GCF of 578 and 584

1. What is the GCF of 578 and 584?

Answer: GCF of 578 and 584 is 2.

2. What are the Factors of 578?

Answer: Factors of 578 are 1, 2, 17, 34, 289, 578. There are 6 integers that are factors of 578. The greatest factor of 578 is 578.

3. What are the Factors of 584?

Answer: Factors of 584 are 1, 2, 4, 8, 73, 146, 292, 584. There are 8 integers that are factors of 584. The greatest factor of 584 is 584.

4. How to Find the GCF of 578 and 584?

Answer:

Greatest Common Factor of 578 and 584 = 2

Step 1: Find the prime factorization of 578

578 = 2 x 17 x 17

Step 2: Find the prime factorization of 584

584 = 2 x 2 x 2 x 73

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

GCF = 2

Step 4: Therefore, the greatest common factor of 578 and 584 is 2