What is the Greatest Common Factor of 65535 and 65553?

Greatest common factor (GCF) of 65535 and 65553 is 3.

GCF(65535,65553) = 3

We will now calculate the prime factors of 65535 and 65553, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65535 and 65553.

How to find the GCF of 65535 and 65553?

We will first find the prime factorization of 65535 and 65553. After we will calculate the factors of 65535 and 65553 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 65553

Prime factors of 65553 are 3, 21851. Prime factorization of 65553 in exponential form is:

65553 = 3¹ × 21851¹

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 65553

List of positive integer factors of 65553 that divides 65535 without a remainder.

1, 3, 21851

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65535 and 65553. The biggest common factor number is the GCF number.
So the greatest common factor 65535 and 65553 is 3.

Also check out the Least Common Multiple of 65535 and 65553