What is the Greatest Common Factor of 580 and 588?

Greatest common factor (GCF) of 580 and 588 is 4.

GCF(580,588) = 4

We will now calculate the prime factors of 580 and 588, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 580 and 588.

How to find the GCF of 580 and 588?

We will first find the prime factorization of 580 and 588. After we will calculate the factors of 580 and 588 and find the biggest common factor number .

Step-1: Prime Factorization of 580

Prime factors of 580 are 2, 5, 29. Prime factorization of 580 in exponential form is:

580 = 2² × 5¹ × 29¹

Step-2: Prime Factorization of 588

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

588 = 2² × 3¹ × 7²

Step-3: Factors of 580

List of positive integer factors of 580 that divides 580 without a remainder.

1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290

Step-4: Factors of 588

List of positive integer factors of 588 that divides 580 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 580 and 588. The biggest common factor number is the GCF number.
So the greatest common factor 580 and 588 is 4.

Also check out the Least Common Multiple of 580 and 588