What is the Greatest Common Factor of 30200 and 30205?

Greatest common factor (GCF) of 30200 and 30205 is 5.

GCF(30200,30205) = 5

We will now calculate the prime factors of 30200 and 30205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30200 and 30205.

How to find the GCF of 30200 and 30205?

We will first find the prime factorization of 30200 and 30205. After we will calculate the factors of 30200 and 30205 and find the biggest common factor number .

Step-1: Prime Factorization of 30200

Prime factors of 30200 are 2, 5, 151. Prime factorization of 30200 in exponential form is:

30200 = 2³ × 5² × 151¹

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 30200

List of positive integer factors of 30200 that divides 30200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 151, 200, 302, 604, 755, 1208, 1510, 3020, 3775, 6040, 7550, 15100

Step-4: Factors of 30205

List of positive integer factors of 30205 that divides 30200 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30200 and 30205. The biggest common factor number is the GCF number.
So the greatest common factor 30200 and 30205 is 5.

Also check out the Least Common Multiple of 30200 and 30205