What is the Greatest Common Factor of 65535 and 65549?

Greatest common factor (GCF) of 65535 and 65549 is 1.

GCF(65535,65549) = 1

We will now calculate the prime factors of 65535 and 65549, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65535 and 65549.

How to find the GCF of 65535 and 65549?

We will first find the prime factorization of 65535 and 65549. After we will calculate the factors of 65535 and 65549 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 65549

Prime factors of 65549 are 11, 59, 101. Prime factorization of 65549 in exponential form is:

65549 = 11¹ × 59¹ × 101¹

Step-3: Factors of 65535

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

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

Step-4: Factors of 65549

List of positive integer factors of 65549 that divides 65535 without a remainder.

1, 11, 59, 101, 649, 1111, 5959

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65535 and 65549. The biggest common factor number is the GCF number.
So the greatest common factor 65535 and 65549 is 1.

Also check out the Least Common Multiple of 65535 and 65549