What is the Greatest Common Factor of 30294 and 30306?

Greatest common factor (GCF) of 30294 and 30306 is 6.

GCF(30294,30306) = 6

We will now calculate the prime factors of 30294 and 30306, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30294 and 30306.

How to find the GCF of 30294 and 30306?

We will first find the prime factorization of 30294 and 30306. After we will calculate the factors of 30294 and 30306 and find the biggest common factor number .

Step-1: Prime Factorization of 30294

Prime factors of 30294 are 2, 3, 11, 17. Prime factorization of 30294 in exponential form is:

30294 = 2¹ × 3⁴ × 11¹ × 17¹

Step-2: 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-3: Factors of 30294

List of positive integer factors of 30294 that divides 30294 without a remainder.

1, 2, 3, 6, 9, 11, 17, 18, 22, 27, 33, 34, 51, 54, 66, 81, 99, 102, 153, 162, 187, 198, 297, 306, 374, 459, 561, 594, 891, 918, 1122, 1377, 1683, 1782, 2754, 3366, 5049, 10098, 15147

Step-4: Factors of 30306

List of positive integer factors of 30306 that divides 30294 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30294 and 30306. The biggest common factor number is the GCF number.
So the greatest common factor 30294 and 30306 is 6.

Also check out the Least Common Multiple of 30294 and 30306