What is the Greatest Common Factor of 27664 and 27678?

Greatest common factor (GCF) of 27664 and 27678 is 14.

GCF(27664,27678) = 14

We will now calculate the prime factors of 27664 and 27678, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27664 and 27678.

How to find the GCF of 27664 and 27678?

We will first find the prime factorization of 27664 and 27678. After we will calculate the factors of 27664 and 27678 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 27678

Prime factors of 27678 are 2, 3, 7, 659. Prime factorization of 27678 in exponential form is:

27678 = 2¹ × 3¹ × 7¹ × 659¹

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 27678

List of positive integer factors of 27678 that divides 27664 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 659, 1318, 1977, 3954, 4613, 9226, 13839

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27664 and 27678. The biggest common factor number is the GCF number.
So the greatest common factor 27664 and 27678 is 14.

Also check out the Least Common Multiple of 27664 and 27678