What is the Greatest Common Factor of 65534 and 65540?

Greatest common factor (GCF) of 65534 and 65540 is 2.

GCF(65534,65540) = 2

We will now calculate the prime factors of 65534 and 65540, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65534 and 65540.

How to find the GCF of 65534 and 65540?

We will first find the prime factorization of 65534 and 65540. After we will calculate the factors of 65534 and 65540 and find the biggest common factor number .

Step-1: Prime Factorization of 65534

Prime factors of 65534 are 2, 7, 31, 151. Prime factorization of 65534 in exponential form is:

65534 = 2¹ × 7¹ × 31¹ × 151¹

Step-2: Prime Factorization of 65540

Prime factors of 65540 are 2, 5, 29, 113. Prime factorization of 65540 in exponential form is:

65540 = 2² × 5¹ × 29¹ × 113¹

Step-3: Factors of 65534

List of positive integer factors of 65534 that divides 65534 without a remainder.

1, 2, 7, 14, 31, 62, 151, 217, 302, 434, 1057, 2114, 4681, 9362, 32767

Step-4: Factors of 65540

List of positive integer factors of 65540 that divides 65534 without a remainder.

1, 2, 4, 5, 10, 20, 29, 58, 113, 116, 145, 226, 290, 452, 565, 580, 1130, 2260, 3277, 6554, 13108, 16385, 32770

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65534 and 65540. The biggest common factor number is the GCF number.
So the greatest common factor 65534 and 65540 is 2.

Also check out the Least Common Multiple of 65534 and 65540