What is the Greatest Common Factor of 55314 and 55328?

Greatest common factor (GCF) of 55314 and 55328 is 14.

GCF(55314,55328) = 14

We will now calculate the prime factors of 55314 and 55328, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 55314 and 55328.

How to find the GCF of 55314 and 55328?

We will first find the prime factorization of 55314 and 55328. After we will calculate the factors of 55314 and 55328 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 55328

Prime factors of 55328 are 2, 7, 13, 19. Prime factorization of 55328 in exponential form is:

55328 = 2⁵ × 7¹ × 13¹ × 19¹

Step-3: Factors of 55314

List of positive integer factors of 55314 that divides 55314 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

Step-4: Factors of 55328

List of positive integer factors of 55328 that divides 55314 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 19, 26, 28, 32, 38, 52, 56, 76, 91, 104, 112, 133, 152, 182, 208, 224, 247, 266, 304, 364, 416, 494, 532, 608, 728, 988, 1064, 1456, 1729, 1976, 2128, 2912, 3458, 3952, 4256, 6916, 7904, 13832, 27664

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 55314 and 55328. The biggest common factor number is the GCF number.
So the greatest common factor 55314 and 55328 is 14.

Also check out the Least Common Multiple of 55314 and 55328