What is the Greatest Common Factor of 30774 and 30780?

Greatest common factor (GCF) of 30774 and 30780 is 6.

GCF(30774,30780) = 6

We will now calculate the prime factors of 30774 and 30780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30774 and 30780.

How to find the GCF of 30774 and 30780?

We will first find the prime factorization of 30774 and 30780. After we will calculate the factors of 30774 and 30780 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 30780

Prime factors of 30780 are 2, 3, 5, 19. Prime factorization of 30780 in exponential form is:

30780 = 2² × 3⁴ × 5¹ × 19¹

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 30780

List of positive integer factors of 30780 that divides 30774 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 27, 30, 36, 38, 45, 54, 57, 60, 76, 81, 90, 95, 108, 114, 135, 162, 171, 180, 190, 228, 270, 285, 324, 342, 380, 405, 513, 540, 570, 684, 810, 855, 1026, 1140, 1539, 1620, 1710, 2052, 2565, 3078, 3420, 5130, 6156, 7695, 10260, 15390

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30774 and 30780. The biggest common factor number is the GCF number.
So the greatest common factor 30774 and 30780 is 6.

Also check out the Least Common Multiple of 30774 and 30780