What is the Greatest Common Factor of 67089 and 67100?

Greatest common factor (GCF) of 67089 and 67100 is 11.

GCF(67089,67100) = 11

We will now calculate the prime factors of 67089 and 67100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67089 and 67100.

How to find the GCF of 67089 and 67100?

We will first find the prime factorization of 67089 and 67100. After we will calculate the factors of 67089 and 67100 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 67100

Prime factors of 67100 are 2, 5, 11, 61. Prime factorization of 67100 in exponential form is:

67100 = 2² × 5² × 11¹ × 61¹

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 67100

List of positive integer factors of 67100 that divides 67089 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 61, 100, 110, 122, 220, 244, 275, 305, 550, 610, 671, 1100, 1220, 1342, 1525, 2684, 3050, 3355, 6100, 6710, 13420, 16775, 33550

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67089 and 67100. The biggest common factor number is the GCF number.
So the greatest common factor 67089 and 67100 is 11.

Also check out the Least Common Multiple of 67089 and 67100