What is the Greatest Common Factor of 65307 and 65312?

Greatest common factor (GCF) of 65307 and 65312 is 1.

GCF(65307,65312) = 1

We will now calculate the prime factors of 65307 and 65312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65307 and 65312.

How to find the GCF of 65307 and 65312?

We will first find the prime factorization of 65307 and 65312. After we will calculate the factors of 65307 and 65312 and find the biggest common factor number .

Step-1: Prime Factorization of 65307

Prime factors of 65307 are 3, 11, 1979. Prime factorization of 65307 in exponential form is:

65307 = 3¹ × 11¹ × 1979¹

Step-2: Prime Factorization of 65312

Prime factors of 65312 are 2, 13, 157. Prime factorization of 65312 in exponential form is:

65312 = 2⁵ × 13¹ × 157¹

Step-3: Factors of 65307

List of positive integer factors of 65307 that divides 65307 without a remainder.

1, 3, 11, 33, 1979, 5937, 21769

Step-4: Factors of 65312

List of positive integer factors of 65312 that divides 65307 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 157, 208, 314, 416, 628, 1256, 2041, 2512, 4082, 5024, 8164, 16328, 32656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65307 and 65312. The biggest common factor number is the GCF number.
So the greatest common factor 65307 and 65312 is 1.

Also check out the Least Common Multiple of 65307 and 65312