What is the Greatest Common Factor of 60306 and 60312?

Greatest common factor (GCF) of 60306 and 60312 is 6.

GCF(60306,60312) = 6

We will now calculate the prime factors of 60306 and 60312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 60306 and 60312.

How to find the GCF of 60306 and 60312?

We will first find the prime factorization of 60306 and 60312. After we will calculate the factors of 60306 and 60312 and find the biggest common factor number .

Step-1: Prime Factorization of 60306

Prime factors of 60306 are 2, 3, 19, 23. Prime factorization of 60306 in exponential form is:

60306 = 2¹ × 3¹ × 19¹ × 23²

Step-2: Prime Factorization of 60312

Prime factors of 60312 are 2, 3, 7, 359. Prime factorization of 60312 in exponential form is:

60312 = 2³ × 3¹ × 7¹ × 359¹

Step-3: Factors of 60306

List of positive integer factors of 60306 that divides 60306 without a remainder.

1, 2, 3, 6, 19, 23, 38, 46, 57, 69, 114, 138, 437, 529, 874, 1058, 1311, 1587, 2622, 3174, 10051, 20102, 30153

Step-4: Factors of 60312

List of positive integer factors of 60312 that divides 60306 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168, 359, 718, 1077, 1436, 2154, 2513, 2872, 4308, 5026, 7539, 8616, 10052, 15078, 20104, 30156

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 60306 and 60312. The biggest common factor number is the GCF number.
So the greatest common factor 60306 and 60312 is 6.

Also check out the Least Common Multiple of 60306 and 60312