What is the Greatest Common Factor of 574 and 588?

Greatest common factor (GCF) of 574 and 588 is 14.

GCF(574,588) = 14

We will now calculate the prime factors of 574 and 588, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 574 and 588.

How to find the GCF of 574 and 588?

We will first find the prime factorization of 574 and 588. After we will calculate the factors of 574 and 588 and find the biggest common factor number .

Step-1: Prime Factorization of 574

Prime factors of 574 are 2, 7, 41. Prime factorization of 574 in exponential form is:

574 = 2¹ × 7¹ × 41¹

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 574

List of positive integer factors of 574 that divides 574 without a remainder.

1, 2, 7, 14, 41, 82, 287

Step-4: Factors of 588

List of positive integer factors of 588 that divides 574 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 574 and 588. The biggest common factor number is the GCF number.
So the greatest common factor 574 and 588 is 14.

Also check out the Least Common Multiple of 574 and 588