What is the Greatest Common Factor of 27664 and 27677?

Greatest common factor (GCF) of 27664 and 27677 is 13.

GCF(27664,27677) = 13

We will now calculate the prime factors of 27664 and 27677, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27664 and 27677.

How to find the GCF of 27664 and 27677?

We will first find the prime factorization of 27664 and 27677. After we will calculate the factors of 27664 and 27677 and find the biggest common factor number .

Step-1: Prime Factorization of 27664

Prime factors of 27664 are 2, 7, 13, 19. Prime factorization of 27664 in exponential form is:

27664 = 2⁴ × 7¹ × 13¹ × 19¹

Step-2: Prime Factorization of 27677

Prime factors of 27677 are 13, 2129. Prime factorization of 27677 in exponential form is:

27677 = 13¹ × 2129¹

Step-3: Factors of 27664

List of positive integer factors of 27664 that divides 27664 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 19, 26, 28, 38, 52, 56, 76, 91, 104, 112, 133, 152, 182, 208, 247, 266, 304, 364, 494, 532, 728, 988, 1064, 1456, 1729, 1976, 2128, 3458, 3952, 6916, 13832

Step-4: Factors of 27677

List of positive integer factors of 27677 that divides 27664 without a remainder.

1, 13, 2129

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27664 and 27677. The biggest common factor number is the GCF number.
So the greatest common factor 27664 and 27677 is 13.

Also check out the Least Common Multiple of 27664 and 27677