What is the Greatest Common Factor of 65509 and 65514?

Greatest common factor (GCF) of 65509 and 65514 is 1.

GCF(65509,65514) = 1

We will now calculate the prime factors of 65509 and 65514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65509 and 65514.

How to find the GCF of 65509 and 65514?

We will first find the prime factorization of 65509 and 65514. After we will calculate the factors of 65509 and 65514 and find the biggest common factor number .

Step-1: Prime Factorization of 65509

Prime factors of 65509 are 109, 601. Prime factorization of 65509 in exponential form is:

65509 = 109¹ × 601¹

Step-2: Prime Factorization of 65514

Prime factors of 65514 are 2, 3, 61, 179. Prime factorization of 65514 in exponential form is:

65514 = 2¹ × 3¹ × 61¹ × 179¹

Step-3: Factors of 65509

List of positive integer factors of 65509 that divides 65509 without a remainder.

1, 109, 601

Step-4: Factors of 65514

List of positive integer factors of 65514 that divides 65509 without a remainder.

1, 2, 3, 6, 61, 122, 179, 183, 358, 366, 537, 1074, 10919, 21838, 32757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65509 and 65514. The biggest common factor number is the GCF number.
So the greatest common factor 65509 and 65514 is 1.

Also check out the Least Common Multiple of 65509 and 65514