What is the Greatest Common Factor of 65307 and 65322?

Greatest common factor (GCF) of 65307 and 65322 is 3.

GCF(65307,65322) = 3

We will now calculate the prime factors of 65307 and 65322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65307 and 65322.

How to find the GCF of 65307 and 65322?

We will first find the prime factorization of 65307 and 65322. After we will calculate the factors of 65307 and 65322 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 65322

Prime factors of 65322 are 2, 3, 19, 191. Prime factorization of 65322 in exponential form is:

65322 = 2¹ × 3² × 19¹ × 191¹

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 65322

List of positive integer factors of 65322 that divides 65307 without a remainder.

1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 191, 342, 382, 573, 1146, 1719, 3438, 3629, 7258, 10887, 21774, 32661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65307 and 65322. The biggest common factor number is the GCF number.
So the greatest common factor 65307 and 65322 is 3.

Also check out the Least Common Multiple of 65307 and 65322