What is the Greatest Common Factor of 27664 and 27680?

Greatest common factor (GCF) of 27664 and 27680 is 16.

GCF(27664,27680) = 16

We will now calculate the prime factors of 27664 and 27680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27664 and 27680.

How to find the GCF of 27664 and 27680?

We will first find the prime factorization of 27664 and 27680. After we will calculate the factors of 27664 and 27680 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 27680

Prime factors of 27680 are 2, 5, 173. Prime factorization of 27680 in exponential form is:

27680 = 2⁵ × 5¹ × 173¹

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 27680

List of positive integer factors of 27680 that divides 27664 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 173, 346, 692, 865, 1384, 1730, 2768, 3460, 5536, 6920, 13840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27664 and 27680. The biggest common factor number is the GCF number.
So the greatest common factor 27664 and 27680 is 16.

Also check out the Least Common Multiple of 27664 and 27680