What is the Greatest Common Factor of 30205 and 30212?

Greatest common factor (GCF) of 30205 and 30212 is 7.

GCF(30205,30212) = 7

We will now calculate the prime factors of 30205 and 30212, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30205 and 30212.

How to find the GCF of 30205 and 30212?

We will first find the prime factorization of 30205 and 30212. After we will calculate the factors of 30205 and 30212 and find the biggest common factor number .

Step-1: Prime Factorization of 30205

Prime factors of 30205 are 5, 7, 863. Prime factorization of 30205 in exponential form is:

30205 = 5¹ × 7¹ × 863¹

Step-2: Prime Factorization of 30212

Prime factors of 30212 are 2, 7, 13, 83. Prime factorization of 30212 in exponential form is:

30212 = 2² × 7¹ × 13¹ × 83¹

Step-3: Factors of 30205

List of positive integer factors of 30205 that divides 30205 without a remainder.

1, 5, 7, 35, 863, 4315, 6041

Step-4: Factors of 30212

List of positive integer factors of 30212 that divides 30205 without a remainder.

1, 2, 4, 7, 13, 14, 26, 28, 52, 83, 91, 166, 182, 332, 364, 581, 1079, 1162, 2158, 2324, 4316, 7553, 15106

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30205 and 30212. The biggest common factor number is the GCF number.
So the greatest common factor 30205 and 30212 is 7.

Also check out the Least Common Multiple of 30205 and 30212