What is the Greatest Common Factor of 65278 and 65296?

Greatest common factor (GCF) of 65278 and 65296 is 2.

GCF(65278,65296) = 2

We will now calculate the prime factors of 65278 and 65296, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65278 and 65296.

How to find the GCF of 65278 and 65296?

We will first find the prime factorization of 65278 and 65296. After we will calculate the factors of 65278 and 65296 and find the biggest common factor number .

Step-1: Prime Factorization of 65278

Prime factors of 65278 are 2, 127, 257. Prime factorization of 65278 in exponential form is:

65278 = 2¹ × 127¹ × 257¹

Step-2: Prime Factorization of 65296

Prime factors of 65296 are 2, 7, 11, 53. Prime factorization of 65296 in exponential form is:

65296 = 2⁴ × 7¹ × 11¹ × 53¹

Step-3: Factors of 65278

List of positive integer factors of 65278 that divides 65278 without a remainder.

1, 2, 127, 254, 257, 514, 32639

Step-4: Factors of 65296

List of positive integer factors of 65296 that divides 65278 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 44, 53, 56, 77, 88, 106, 112, 154, 176, 212, 308, 371, 424, 583, 616, 742, 848, 1166, 1232, 1484, 2332, 2968, 4081, 4664, 5936, 8162, 9328, 16324, 32648

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65278 and 65296. The biggest common factor number is the GCF number.
So the greatest common factor 65278 and 65296 is 2.

Also check out the Least Common Multiple of 65278 and 65296