What is the Greatest Common Factor of 30305 and 30310?

Greatest common factor (GCF) of 30305 and 30310 is 5.

GCF(30305,30310) = 5

We will now calculate the prime factors of 30305 and 30310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30305 and 30310.

How to find the GCF of 30305 and 30310?

We will first find the prime factorization of 30305 and 30310. After we will calculate the factors of 30305 and 30310 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30310

Prime factors of 30310 are 2, 5, 7, 433. Prime factorization of 30310 in exponential form is:

30310 = 2¹ × 5¹ × 7¹ × 433¹

Step-3: Factors of 30305

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

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

Step-4: Factors of 30310

List of positive integer factors of 30310 that divides 30305 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 433, 866, 2165, 3031, 4330, 6062, 15155

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30305 and 30310. The biggest common factor number is the GCF number.
So the greatest common factor 30305 and 30310 is 5.

Also check out the Least Common Multiple of 30305 and 30310