What is the Greatest Common Factor of 30200 and 30210?

Greatest common factor (GCF) of 30200 and 30210 is 10.

GCF(30200,30210) = 10

We will now calculate the prime factors of 30200 and 30210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30200 and 30210.

How to find the GCF of 30200 and 30210?

We will first find the prime factorization of 30200 and 30210. After we will calculate the factors of 30200 and 30210 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 30210

Prime factors of 30210 are 2, 3, 5, 19, 53. Prime factorization of 30210 in exponential form is:

30210 = 2¹ × 3¹ × 5¹ × 19¹ × 53¹

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 30210

List of positive integer factors of 30210 that divides 30200 without a remainder.

1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 53, 57, 95, 106, 114, 159, 190, 265, 285, 318, 530, 570, 795, 1007, 1590, 2014, 3021, 5035, 6042, 10070, 15105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30200 and 30210. The biggest common factor number is the GCF number.
So the greatest common factor 30200 and 30210 is 10.

Also check out the Least Common Multiple of 30200 and 30210