What is the Greatest Common Factor of 65529 and 65535?

Greatest common factor (GCF) of 65529 and 65535 is 3.

GCF(65529,65535) = 3

We will now calculate the prime factors of 65529 and 65535, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65529 and 65535.

How to find the GCF of 65529 and 65535?

We will first find the prime factorization of 65529 and 65535. After we will calculate the factors of 65529 and 65535 and find the biggest common factor number .

Step-1: Prime Factorization of 65529

Prime factors of 65529 are 3, 809. Prime factorization of 65529 in exponential form is:

65529 = 3⁴ × 809¹

Step-2: Prime Factorization of 65535

Prime factors of 65535 are 3, 5, 17, 257. Prime factorization of 65535 in exponential form is:

65535 = 3¹ × 5¹ × 17¹ × 257¹

Step-3: Factors of 65529

List of positive integer factors of 65529 that divides 65529 without a remainder.

1, 3, 9, 27, 81, 809, 2427, 7281, 21843

Step-4: Factors of 65535

List of positive integer factors of 65535 that divides 65529 without a remainder.

1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65529 and 65535. The biggest common factor number is the GCF number.
So the greatest common factor 65529 and 65535 is 3.

Also check out the Least Common Multiple of 65529 and 65535