What is the Greatest Common Factor of 65296 and 65310?

Greatest common factor (GCF) of 65296 and 65310 is 14.

GCF(65296,65310) = 14

We will now calculate the prime factors of 65296 and 65310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65296 and 65310.

How to find the GCF of 65296 and 65310?

We will first find the prime factorization of 65296 and 65310. After we will calculate the factors of 65296 and 65310 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 65310

Prime factors of 65310 are 2, 3, 5, 7, 311. Prime factorization of 65310 in exponential form is:

65310 = 2¹ × 3¹ × 5¹ × 7¹ × 311¹

Step-3: Factors of 65296

List of positive integer factors of 65296 that divides 65296 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

Step-4: Factors of 65310

List of positive integer factors of 65310 that divides 65296 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210, 311, 622, 933, 1555, 1866, 2177, 3110, 4354, 4665, 6531, 9330, 10885, 13062, 21770, 32655

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65296 and 65310. The biggest common factor number is the GCF number.
So the greatest common factor 65296 and 65310 is 14.

Also check out the Least Common Multiple of 65296 and 65310