What is the Greatest Common Factor of 65994 and 66009?

Greatest common factor (GCF) of 65994 and 66009 is 3.

GCF(65994,66009) = 3

We will now calculate the prime factors of 65994 and 66009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65994 and 66009.

How to find the GCF of 65994 and 66009?

We will first find the prime factorization of 65994 and 66009. After we will calculate the factors of 65994 and 66009 and find the biggest common factor number .

Step-1: Prime Factorization of 65994

Prime factors of 65994 are 2, 3, 17, 647. Prime factorization of 65994 in exponential form is:

65994 = 2¹ × 3¹ × 17¹ × 647¹

Step-2: Prime Factorization of 66009

Prime factors of 66009 are 3, 22003. Prime factorization of 66009 in exponential form is:

66009 = 3¹ × 22003¹

Step-3: Factors of 65994

List of positive integer factors of 65994 that divides 65994 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 647, 1294, 1941, 3882, 10999, 21998, 32997

Step-4: Factors of 66009

List of positive integer factors of 66009 that divides 65994 without a remainder.

1, 3, 22003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65994 and 66009. The biggest common factor number is the GCF number.
So the greatest common factor 65994 and 66009 is 3.

Also check out the Least Common Multiple of 65994 and 66009