What is the Greatest Common Factor of 54315 and 54320?

Greatest common factor (GCF) of 54315 and 54320 is 5.

GCF(54315,54320) = 5

We will now calculate the prime factors of 54315 and 54320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54315 and 54320.

How to find the GCF of 54315 and 54320?

We will first find the prime factorization of 54315 and 54320. After we will calculate the factors of 54315 and 54320 and find the biggest common factor number .

Step-1: Prime Factorization of 54315

Prime factors of 54315 are 3, 5, 17, 71. Prime factorization of 54315 in exponential form is:

54315 = 3² × 5¹ × 17¹ × 71¹

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 54315

List of positive integer factors of 54315 that divides 54315 without a remainder.

1, 3, 5, 9, 15, 17, 45, 51, 71, 85, 153, 213, 255, 355, 639, 765, 1065, 1207, 3195, 3621, 6035, 10863, 18105

Step-4: Factors of 54320

List of positive integer factors of 54320 that divides 54315 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 54315 and 54320. The biggest common factor number is the GCF number.
So the greatest common factor 54315 and 54320 is 5.

Also check out the Least Common Multiple of 54315 and 54320