What is the Greatest Common Factor of 65009 and 65025?

Greatest common factor (GCF) of 65009 and 65025 is 1.

GCF(65009,65025) = 1

We will now calculate the prime factors of 65009 and 65025, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65009 and 65025.

How to find the GCF of 65009 and 65025?

We will first find the prime factorization of 65009 and 65025. After we will calculate the factors of 65009 and 65025 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 65025

Prime factors of 65025 are 3, 5, 17. Prime factorization of 65025 in exponential form is:

65025 = 3² × 5² × 17²

Step-3: Factors of 65009

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

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

Step-4: Factors of 65025

List of positive integer factors of 65025 that divides 65009 without a remainder.

1, 3, 5, 9, 15, 17, 25, 45, 51, 75, 85, 153, 225, 255, 289, 425, 765, 867, 1275, 1445, 2601, 3825, 4335, 7225, 13005, 21675

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65009 and 65025. The biggest common factor number is the GCF number.
So the greatest common factor 65009 and 65025 is 1.

Also check out the Least Common Multiple of 65009 and 65025