What is the Greatest Common Factor of 66589 and 66606?

Greatest common factor (GCF) of 66589 and 66606 is 17.

GCF(66589,66606) = 17

We will now calculate the prime factors of 66589 and 66606, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 66589 and 66606.

How to find the GCF of 66589 and 66606?

We will first find the prime factorization of 66589 and 66606. After we will calculate the factors of 66589 and 66606 and find the biggest common factor number .

Step-1: Prime Factorization of 66589

Prime factors of 66589 are 17, 3917. Prime factorization of 66589 in exponential form is:

66589 = 17¹ × 3917¹

Step-2: Prime Factorization of 66606

Prime factors of 66606 are 2, 3, 17, 653. Prime factorization of 66606 in exponential form is:

66606 = 2¹ × 3¹ × 17¹ × 653¹

Step-3: Factors of 66589

List of positive integer factors of 66589 that divides 66589 without a remainder.

1, 17, 3917

Step-4: Factors of 66606

List of positive integer factors of 66606 that divides 66589 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 653, 1306, 1959, 3918, 11101, 22202, 33303

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 66589 and 66606. The biggest common factor number is the GCF number.
So the greatest common factor 66589 and 66606 is 17.

Also check out the Least Common Multiple of 66589 and 66606