What is the Greatest Common Factor of 27648 and 27664?

Greatest common factor (GCF) of 27648 and 27664 is 16.

GCF(27648,27664) = 16

We will now calculate the prime factors of 27648 and 27664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27648 and 27664.

How to find the GCF of 27648 and 27664?

We will first find the prime factorization of 27648 and 27664. After we will calculate the factors of 27648 and 27664 and find the biggest common factor number .

Step-1: Prime Factorization of 27648

Prime factors of 27648 are 2, 3. Prime factorization of 27648 in exponential form is:

27648 = 2¹⁰ × 3³

Step-2: 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-3: Factors of 27648

List of positive integer factors of 27648 that divides 27648 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1024, 1152, 1536, 1728, 2304, 3072, 3456, 4608, 6912, 9216, 13824

Step-4: Factors of 27664

List of positive integer factors of 27664 that divides 27648 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27648 and 27664. The biggest common factor number is the GCF number.
So the greatest common factor 27648 and 27664 is 16.

Also check out the Least Common Multiple of 27648 and 27664