What is the Greatest Common Factor of 54306 and 54320?

Greatest common factor (GCF) of 54306 and 54320 is 14.

GCF(54306,54320) = 14

We will now calculate the prime factors of 54306 and 54320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54306 and 54320.

How to find the GCF of 54306 and 54320?

We will first find the prime factorization of 54306 and 54320. After we will calculate the factors of 54306 and 54320 and find the biggest common factor number .

Step-1: Prime Factorization of 54306

Prime factors of 54306 are 2, 3, 7, 431. Prime factorization of 54306 in exponential form is:

54306 = 2¹ × 3² × 7¹ × 431¹

Step-2: Prime Factorization of 54320

Prime factors of 54320 are 2, 5, 7, 97. Prime factorization of 54320 in exponential form is:

54320 = 2⁴ × 5¹ × 7¹ × 97¹

Step-3: Factors of 54306

List of positive integer factors of 54306 that divides 54306 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 431, 862, 1293, 2586, 3017, 3879, 6034, 7758, 9051, 18102, 27153

Step-4: Factors of 54320

List of positive integer factors of 54320 that divides 54306 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 97, 112, 140, 194, 280, 388, 485, 560, 679, 776, 970, 1358, 1552, 1940, 2716, 3395, 3880, 5432, 6790, 7760, 10864, 13580, 27160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54306 and 54320. The biggest common factor number is the GCF number.
So the greatest common factor 54306 and 54320 is 14.

Also check out the Least Common Multiple of 54306 and 54320