What is the Greatest Common Factor of 77805 and 77824?

Greatest common factor (GCF) of 77805 and 77824 is 19.

GCF(77805,77824) = 19

We will now calculate the prime factors of 77805 and 77824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77805 and 77824.

How to find the GCF of 77805 and 77824?

We will first find the prime factorization of 77805 and 77824. After we will calculate the factors of 77805 and 77824 and find the biggest common factor number .

Step-1: Prime Factorization of 77805

Prime factors of 77805 are 3, 5, 7, 13, 19. Prime factorization of 77805 in exponential form is:

77805 = 3² × 5¹ × 7¹ × 13¹ × 19¹

Step-2: Prime Factorization of 77824

Prime factors of 77824 are 2, 19. Prime factorization of 77824 in exponential form is:

77824 = 2¹² × 19¹

Step-3: Factors of 77805

List of positive integer factors of 77805 that divides 77805 without a remainder.

1, 3, 5, 7, 9, 13, 15, 19, 21, 35, 39, 45, 57, 63, 65, 91, 95, 105, 117, 133, 171, 195, 247, 273, 285, 315, 399, 455, 585, 665, 741, 819, 855, 1197, 1235, 1365, 1729, 1995, 2223, 3705, 4095, 5187, 5985, 8645, 11115, 15561, 25935

Step-4: Factors of 77824

List of positive integer factors of 77824 that divides 77805 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1024, 1216, 2048, 2432, 4096, 4864, 9728, 19456, 38912

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77805 and 77824. The biggest common factor number is the GCF number.
So the greatest common factor 77805 and 77824 is 19.

Also check out the Least Common Multiple of 77805 and 77824