What is the Greatest Common Factor of 30198 and 30205?

Greatest common factor (GCF) of 30198 and 30205 is 7.

GCF(30198,30205) = 7

We will now calculate the prime factors of 30198 and 30205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30198 and 30205.

How to find the GCF of 30198 and 30205?

We will first find the prime factorization of 30198 and 30205. After we will calculate the factors of 30198 and 30205 and find the biggest common factor number .

Step-1: Prime Factorization of 30198

Prime factors of 30198 are 2, 3, 7, 719. Prime factorization of 30198 in exponential form is:

30198 = 2¹ × 3¹ × 7¹ × 719¹

Step-2: 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-3: Factors of 30198

List of positive integer factors of 30198 that divides 30198 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 719, 1438, 2157, 4314, 5033, 10066, 15099

Step-4: Factors of 30205

List of positive integer factors of 30205 that divides 30198 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30198 and 30205. The biggest common factor number is the GCF number.
So the greatest common factor 30198 and 30205 is 7.

Also check out the Least Common Multiple of 30198 and 30205