What is the Greatest Common Factor of 67089 and 67108?

Greatest common factor (GCF) of 67089 and 67108 is 19.

GCF(67089,67108) = 19

We will now calculate the prime factors of 67089 and 67108, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67089 and 67108.

How to find the GCF of 67089 and 67108?

We will first find the prime factorization of 67089 and 67108. After we will calculate the factors of 67089 and 67108 and find the biggest common factor number .

Step-1: Prime Factorization of 67089

Prime factors of 67089 are 3, 11, 19, 107. Prime factorization of 67089 in exponential form is:

67089 = 3¹ × 11¹ × 19¹ × 107¹

Step-2: Prime Factorization of 67108

Prime factors of 67108 are 2, 19, 883. Prime factorization of 67108 in exponential form is:

67108 = 2² × 19¹ × 883¹

Step-3: Factors of 67089

List of positive integer factors of 67089 that divides 67089 without a remainder.

1, 3, 11, 19, 33, 57, 107, 209, 321, 627, 1177, 2033, 3531, 6099, 22363

Step-4: Factors of 67108

List of positive integer factors of 67108 that divides 67089 without a remainder.

1, 2, 4, 19, 38, 76, 883, 1766, 3532, 16777, 33554

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67089 and 67108. The biggest common factor number is the GCF number.
So the greatest common factor 67089 and 67108 is 19.

Also check out the Least Common Multiple of 67089 and 67108