What is the Greatest Common Factor of 27634 and 27648?

Greatest common factor (GCF) of 27634 and 27648 is 2.

GCF(27634,27648) = 2

We will now calculate the prime factors of 27634 and 27648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27634 and 27648.

How to find the GCF of 27634 and 27648?

We will first find the prime factorization of 27634 and 27648. After we will calculate the factors of 27634 and 27648 and find the biggest common factor number .

Step-1: Prime Factorization of 27634

Prime factors of 27634 are 2, 41, 337. Prime factorization of 27634 in exponential form is:

27634 = 2¹ × 41¹ × 337¹

Step-2: Prime Factorization of 27648

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

27648 = 2¹⁰ × 3³

Step-3: Factors of 27634

List of positive integer factors of 27634 that divides 27634 without a remainder.

1, 2, 41, 82, 337, 674, 13817

Step-4: Factors of 27648

List of positive integer factors of 27648 that divides 27634 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27634 and 27648. The biggest common factor number is the GCF number.
So the greatest common factor 27634 and 27648 is 2.

Also check out the Least Common Multiple of 27634 and 27648