What is the Greatest Common Factor of 29574 and 29589?

Greatest common factor (GCF) of 29574 and 29589 is 3.

GCF(29574,29589) = 3

We will now calculate the prime factors of 29574 and 29589, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29574 and 29589.

How to find the GCF of 29574 and 29589?

We will first find the prime factorization of 29574 and 29589. After we will calculate the factors of 29574 and 29589 and find the biggest common factor number .

Step-1: Prime Factorization of 29574

Prime factors of 29574 are 2, 3, 31, 53. Prime factorization of 29574 in exponential form is:

29574 = 2¹ × 3² × 31¹ × 53¹

Step-2: Prime Factorization of 29589

Prime factors of 29589 are 3, 7, 1409. Prime factorization of 29589 in exponential form is:

29589 = 3¹ × 7¹ × 1409¹

Step-3: Factors of 29574

List of positive integer factors of 29574 that divides 29574 without a remainder.

1, 2, 3, 6, 9, 18, 31, 53, 62, 93, 106, 159, 186, 279, 318, 477, 558, 954, 1643, 3286, 4929, 9858, 14787

Step-4: Factors of 29589

List of positive integer factors of 29589 that divides 29574 without a remainder.

1, 3, 7, 21, 1409, 4227, 9863

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29574 and 29589. The biggest common factor number is the GCF number.
So the greatest common factor 29574 and 29589 is 3.

Also check out the Least Common Multiple of 29574 and 29589