What is the Greatest Common Factor of 55296 and 55314?

Greatest common factor (GCF) of 55296 and 55314 is 18.

GCF(55296,55314) = 18

We will now calculate the prime factors of 55296 and 55314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 55296 and 55314.

How to find the GCF of 55296 and 55314?

We will first find the prime factorization of 55296 and 55314. After we will calculate the factors of 55296 and 55314 and find the biggest common factor number .

Step-1: Prime Factorization of 55296

Prime factors of 55296 are 2, 3. Prime factorization of 55296 in exponential form is:

55296 = 2¹¹ × 3³

Step-2: Prime Factorization of 55314

Prime factors of 55314 are 2, 3, 7, 439. Prime factorization of 55314 in exponential form is:

55314 = 2¹ × 3² × 7¹ × 439¹

Step-3: Factors of 55296

List of positive integer factors of 55296 that divides 55296 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, 2048, 2304, 3072, 3456, 4608, 6144, 6912, 9216, 13824, 18432, 27648

Step-4: Factors of 55314

List of positive integer factors of 55314 that divides 55296 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 439, 878, 1317, 2634, 3073, 3951, 6146, 7902, 9219, 18438, 27657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 55296 and 55314. The biggest common factor number is the GCF number.
So the greatest common factor 55296 and 55314 is 18.

Also check out the Least Common Multiple of 55296 and 55314