What is the Greatest Common Factor of 30320 and 30338?

Greatest common factor (GCF) of 30320 and 30338 is 2.

GCF(30320,30338) = 2

We will now calculate the prime factors of 30320 and 30338, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30320 and 30338.

How to find the GCF of 30320 and 30338?

We will first find the prime factorization of 30320 and 30338. After we will calculate the factors of 30320 and 30338 and find the biggest common factor number .

Step-1: Prime Factorization of 30320

Prime factors of 30320 are 2, 5, 379. Prime factorization of 30320 in exponential form is:

30320 = 2⁴ × 5¹ × 379¹

Step-2: Prime Factorization of 30338

Prime factors of 30338 are 2, 7, 11, 197. Prime factorization of 30338 in exponential form is:

30338 = 2¹ × 7¹ × 11¹ × 197¹

Step-3: Factors of 30320

List of positive integer factors of 30320 that divides 30320 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 379, 758, 1516, 1895, 3032, 3790, 6064, 7580, 15160

Step-4: Factors of 30338

List of positive integer factors of 30338 that divides 30320 without a remainder.

1, 2, 7, 11, 14, 22, 77, 154, 197, 394, 1379, 2167, 2758, 4334, 15169

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30320 and 30338. The biggest common factor number is the GCF number.
So the greatest common factor 30320 and 30338 is 2.

Also check out the Least Common Multiple of 30320 and 30338