What is the Greatest Common Factor of 27648 and 27660?

Greatest common factor (GCF) of 27648 and 27660 is 12.

GCF(27648,27660) = 12

We will now calculate the prime factors of 27648 and 27660, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27648 and 27660.

How to find the GCF of 27648 and 27660?

We will first find the prime factorization of 27648 and 27660. After we will calculate the factors of 27648 and 27660 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 27660

Prime factors of 27660 are 2, 3, 5, 461. Prime factorization of 27660 in exponential form is:

27660 = 2² × 3¹ × 5¹ × 461¹

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 27660

List of positive integer factors of 27660 that divides 27648 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 461, 922, 1383, 1844, 2305, 2766, 4610, 5532, 6915, 9220, 13830

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27648 and 27660. The biggest common factor number is the GCF number.
So the greatest common factor 27648 and 27660 is 12.

Also check out the Least Common Multiple of 27648 and 27660