What is the Greatest Common Factor of 54684 and 54698?

Greatest common factor (GCF) of 54684 and 54698 is 14.

GCF(54684,54698) = 14

We will now calculate the prime factors of 54684 and 54698, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54684 and 54698.

How to find the GCF of 54684 and 54698?

We will first find the prime factorization of 54684 and 54698. After we will calculate the factors of 54684 and 54698 and find the biggest common factor number .

Step-1: Prime Factorization of 54684

Prime factors of 54684 are 2, 3, 7, 31. Prime factorization of 54684 in exponential form is:

54684 = 2² × 3² × 7² × 31¹

Step-2: Prime Factorization of 54698

Prime factors of 54698 are 2, 7, 3907. Prime factorization of 54698 in exponential form is:

54698 = 2¹ × 7¹ × 3907¹

Step-3: Factors of 54684

List of positive integer factors of 54684 that divides 54684 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 31, 36, 42, 49, 62, 63, 84, 93, 98, 124, 126, 147, 186, 196, 217, 252, 279, 294, 372, 434, 441, 558, 588, 651, 868, 882, 1116, 1302, 1519, 1764, 1953, 2604, 3038, 3906, 4557, 6076, 7812, 9114, 13671, 18228, 27342

Step-4: Factors of 54698

List of positive integer factors of 54698 that divides 54684 without a remainder.

1, 2, 7, 14, 3907, 7814, 27349

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54684 and 54698. The biggest common factor number is the GCF number.
So the greatest common factor 54684 and 54698 is 14.

Also check out the Least Common Multiple of 54684 and 54698