What is the Greatest Common Factor of 30306 and 30321?

Greatest common factor (GCF) of 30306 and 30321 is 3.

GCF(30306,30321) = 3

We will now calculate the prime factors of 30306 and 30321, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30306 and 30321.

How to find the GCF of 30306 and 30321?

We will first find the prime factorization of 30306 and 30321. After we will calculate the factors of 30306 and 30321 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 30321

Prime factors of 30321 are 3, 1123. Prime factorization of 30321 in exponential form is:

30321 = 3³ × 1123¹

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 30321

List of positive integer factors of 30321 that divides 30306 without a remainder.

1, 3, 9, 27, 1123, 3369, 10107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30306 and 30321. The biggest common factor number is the GCF number.
So the greatest common factor 30306 and 30321 is 3.

Also check out the Least Common Multiple of 30306 and 30321