What is the Greatest Common Factor of 54189 and 54208?

Greatest common factor (GCF) of 54189 and 54208 is 1.

GCF(54189,54208) = 1

We will now calculate the prime factors of 54189 and 54208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54189 and 54208.

How to find the GCF of 54189 and 54208?

We will first find the prime factorization of 54189 and 54208. After we will calculate the factors of 54189 and 54208 and find the biggest common factor number .

Step-1: Prime Factorization of 54189

Prime factors of 54189 are 3, 223. Prime factorization of 54189 in exponential form is:

54189 = 3⁵ × 223¹

Step-2: Prime Factorization of 54208

Prime factors of 54208 are 2, 7, 11. Prime factorization of 54208 in exponential form is:

54208 = 2⁶ × 7¹ × 11²

Step-3: Factors of 54189

List of positive integer factors of 54189 that divides 54189 without a remainder.

1, 3, 9, 27, 81, 223, 243, 669, 2007, 6021, 18063

Step-4: Factors of 54208

List of positive integer factors of 54208 that divides 54189 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 32, 44, 56, 64, 77, 88, 112, 121, 154, 176, 224, 242, 308, 352, 448, 484, 616, 704, 847, 968, 1232, 1694, 1936, 2464, 3388, 3872, 4928, 6776, 7744, 13552, 27104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54189 and 54208. The biggest common factor number is the GCF number.
So the greatest common factor 54189 and 54208 is 1.

Also check out the Least Common Multiple of 54189 and 54208