What is the Greatest Common Factor of 30192 and 30209?

Greatest common factor (GCF) of 30192 and 30209 is 17.

GCF(30192,30209) = 17

We will now calculate the prime factors of 30192 and 30209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30192 and 30209.

How to find the GCF of 30192 and 30209?

We will first find the prime factorization of 30192 and 30209. After we will calculate the factors of 30192 and 30209 and find the biggest common factor number .

Step-1: Prime Factorization of 30192

Prime factors of 30192 are 2, 3, 17, 37. Prime factorization of 30192 in exponential form is:

30192 = 2⁴ × 3¹ × 17¹ × 37¹

Step-2: Prime Factorization of 30209

Prime factors of 30209 are 17, 1777. Prime factorization of 30209 in exponential form is:

30209 = 17¹ × 1777¹

Step-3: Factors of 30192

List of positive integer factors of 30192 that divides 30192 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 37, 48, 51, 68, 74, 102, 111, 136, 148, 204, 222, 272, 296, 408, 444, 592, 629, 816, 888, 1258, 1776, 1887, 2516, 3774, 5032, 7548, 10064, 15096

Step-4: Factors of 30209

List of positive integer factors of 30209 that divides 30192 without a remainder.

1, 17, 1777

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30192 and 30209. The biggest common factor number is the GCF number.
So the greatest common factor 30192 and 30209 is 17.

Also check out the Least Common Multiple of 30192 and 30209