What is the Greatest Common Factor of 30774 and 30789?

Greatest common factor (GCF) of 30774 and 30789 is 3.

GCF(30774,30789) = 3

We will now calculate the prime factors of 30774 and 30789, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30774 and 30789.

How to find the GCF of 30774 and 30789?

We will first find the prime factorization of 30774 and 30789. After we will calculate the factors of 30774 and 30789 and find the biggest common factor number .

Step-1: Prime Factorization of 30774

Prime factors of 30774 are 2, 3, 23, 223. Prime factorization of 30774 in exponential form is:

30774 = 2¹ × 3¹ × 23¹ × 223¹

Step-2: Prime Factorization of 30789

Prime factors of 30789 are 3, 11, 311. Prime factorization of 30789 in exponential form is:

30789 = 3² × 11¹ × 311¹

Step-3: Factors of 30774

List of positive integer factors of 30774 that divides 30774 without a remainder.

1, 2, 3, 6, 23, 46, 69, 138, 223, 446, 669, 1338, 5129, 10258, 15387

Step-4: Factors of 30789

List of positive integer factors of 30789 that divides 30774 without a remainder.

1, 3, 9, 11, 33, 99, 311, 933, 2799, 3421, 10263

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30774 and 30789. The biggest common factor number is the GCF number.
So the greatest common factor 30774 and 30789 is 3.

Also check out the Least Common Multiple of 30774 and 30789