What is the Greatest Common Factor of 30294 and 30305?

Greatest common factor (GCF) of 30294 and 30305 is 11.

GCF(30294,30305) = 11

We will now calculate the prime factors of 30294 and 30305, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30294 and 30305.

How to find the GCF of 30294 and 30305?

We will first find the prime factorization of 30294 and 30305. After we will calculate the factors of 30294 and 30305 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 30305

Prime factors of 30305 are 5, 11, 19, 29. Prime factorization of 30305 in exponential form is:

30305 = 5¹ × 11¹ × 19¹ × 29¹

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 30305

List of positive integer factors of 30305 that divides 30294 without a remainder.

1, 5, 11, 19, 29, 55, 95, 145, 209, 319, 551, 1045, 1595, 2755, 6061

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30294 and 30305. The biggest common factor number is the GCF number.
So the greatest common factor 30294 and 30305 is 11.

Also check out the Least Common Multiple of 30294 and 30305