What is the Greatest Common Factor of 30760 and 30780?

Greatest common factor (GCF) of 30760 and 30780 is 20.

GCF(30760,30780) = 20

We will now calculate the prime factors of 30760 and 30780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30760 and 30780.

How to find the GCF of 30760 and 30780?

We will first find the prime factorization of 30760 and 30780. After we will calculate the factors of 30760 and 30780 and find the biggest common factor number .

Step-1: Prime Factorization of 30760

Prime factors of 30760 are 2, 5, 769. Prime factorization of 30760 in exponential form is:

30760 = 2³ × 5¹ × 769¹

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 30760

List of positive integer factors of 30760 that divides 30760 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 769, 1538, 3076, 3845, 6152, 7690, 15380

Step-4: Factors of 30780

List of positive integer factors of 30780 that divides 30760 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 30760 and 30780. The biggest common factor number is the GCF number.
So the greatest common factor 30760 and 30780 is 20.

Also check out the Least Common Multiple of 30760 and 30780