What is the Greatest Common Factor of 65001 and 65009?

Greatest common factor (GCF) of 65001 and 65009 is 1.

GCF(65001,65009) = 1

We will now calculate the prime factors of 65001 and 65009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65001 and 65009.

How to find the GCF of 65001 and 65009?

We will first find the prime factorization of 65001 and 65009. After we will calculate the factors of 65001 and 65009 and find the biggest common factor number .

Step-1: Prime Factorization of 65001

Prime factors of 65001 are 3, 47, 461. Prime factorization of 65001 in exponential form is:

65001 = 3¹ × 47¹ × 461¹

Step-2: Prime Factorization of 65009

Prime factors of 65009 are 7, 37, 251. Prime factorization of 65009 in exponential form is:

65009 = 7¹ × 37¹ × 251¹

Step-3: Factors of 65001

List of positive integer factors of 65001 that divides 65001 without a remainder.

1, 3, 47, 141, 461, 1383, 21667

Step-4: Factors of 65009

List of positive integer factors of 65009 that divides 65001 without a remainder.

1, 7, 37, 251, 259, 1757, 9287

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65001 and 65009. The biggest common factor number is the GCF number.
So the greatest common factor 65001 and 65009 is 1.

Also check out the Least Common Multiple of 65001 and 65009