What is the Greatest Common Factor of 590 and 605?

Greatest common factor (GCF) of 590 and 605 is 5.

GCF(590,605) = 5

We will now calculate the prime factors of 590 and 605, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 590 and 605.

How to find the GCF of 590 and 605?

We will first find the prime factorization of 590 and 605. After we will calculate the factors of 590 and 605 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 605

Prime factors of 605 are 5, 11. Prime factorization of 605 in exponential form is:

605 = 5¹ × 11²

Step-3: Factors of 590

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

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

Step-4: Factors of 605

List of positive integer factors of 605 that divides 590 without a remainder.

1, 5, 11, 55, 121

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 590 and 605. The biggest common factor number is the GCF number.
So the greatest common factor 590 and 605 is 5.

Also check out the Least Common Multiple of 590 and 605