What is the Greatest Common Factor of 580 and 590?

Greatest common factor (GCF) of 580 and 590 is 10.

GCF(580,590) = 10

We will now calculate the prime factors of 580 and 590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 580 and 590.

How to find the GCF of 580 and 590?

We will first find the prime factorization of 580 and 590. After we will calculate the factors of 580 and 590 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 590

Prime factors of 590 are 2, 5, 59. Prime factorization of 590 in exponential form is:

590 = 2¹ × 5¹ × 59¹

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 590

List of positive integer factors of 590 that divides 580 without a remainder.

1, 2, 5, 10, 59, 118, 295

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 580 and 590. The biggest common factor number is the GCF number.
So the greatest common factor 580 and 590 is 10.

Also check out the Least Common Multiple of 580 and 590