What is the Greatest Common Factor of 30306 and 30312?

Greatest common factor (GCF) of 30306 and 30312 is 6.

GCF(30306,30312) = 6

We will now calculate the prime factors of 30306 and 30312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30306 and 30312.

How to find the GCF of 30306 and 30312?

We will first find the prime factorization of 30306 and 30312. After we will calculate the factors of 30306 and 30312 and find the biggest common factor number .

Step-1: Prime Factorization of 30306

Prime factors of 30306 are 2, 3, 5051. Prime factorization of 30306 in exponential form is:

30306 = 2¹ × 3¹ × 5051¹

Step-2: Prime Factorization of 30312

Prime factors of 30312 are 2, 3, 421. Prime factorization of 30312 in exponential form is:

30312 = 2³ × 3² × 421¹

Step-3: Factors of 30306

List of positive integer factors of 30306 that divides 30306 without a remainder.

1, 2, 3, 6, 5051, 10102, 15153

Step-4: Factors of 30312

List of positive integer factors of 30312 that divides 30306 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 421, 842, 1263, 1684, 2526, 3368, 3789, 5052, 7578, 10104, 15156

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30306 and 30312. The biggest common factor number is the GCF number.
So the greatest common factor 30306 and 30312 is 6.

Also check out the Least Common Multiple of 30306 and 30312