What is the Greatest Common Factor of 54301 and 54314?

Greatest common factor (GCF) of 54301 and 54314 is 13.

GCF(54301,54314) = 13

We will now calculate the prime factors of 54301 and 54314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54301 and 54314.

How to find the GCF of 54301 and 54314?

We will first find the prime factorization of 54301 and 54314. After we will calculate the factors of 54301 and 54314 and find the biggest common factor number .

Step-1: Prime Factorization of 54301

Prime factors of 54301 are 13, 4177. Prime factorization of 54301 in exponential form is:

54301 = 13¹ × 4177¹

Step-2: Prime Factorization of 54314

Prime factors of 54314 are 2, 13, 2089. Prime factorization of 54314 in exponential form is:

54314 = 2¹ × 13¹ × 2089¹

Step-3: Factors of 54301

List of positive integer factors of 54301 that divides 54301 without a remainder.

1, 13, 4177

Step-4: Factors of 54314

List of positive integer factors of 54314 that divides 54301 without a remainder.

1, 2, 13, 26, 2089, 4178, 27157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54301 and 54314. The biggest common factor number is the GCF number.
So the greatest common factor 54301 and 54314 is 13.

Also check out the Least Common Multiple of 54301 and 54314