What is the Greatest Common Factor of 19180 and 19200?

Greatest common factor (GCF) of 19180 and 19200 is 20.

GCF(19180,19200) = 20

We will now calculate the prime factors of 19180 and 19200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19180 and 19200.

How to find the GCF of 19180 and 19200?

We will first find the prime factorization of 19180 and 19200. After we will calculate the factors of 19180 and 19200 and find the biggest common factor number .

Step-1: Prime Factorization of 19180

Prime factors of 19180 are 2, 5, 7, 137. Prime factorization of 19180 in exponential form is:

19180 = 2² × 5¹ × 7¹ × 137¹

Step-2: Prime Factorization of 19200

Prime factors of 19200 are 2, 3, 5. Prime factorization of 19200 in exponential form is:

19200 = 2⁸ × 3¹ × 5²

Step-3: Factors of 19180

List of positive integer factors of 19180 that divides 19180 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 137, 140, 274, 548, 685, 959, 1370, 1918, 2740, 3836, 4795, 9590

Step-4: Factors of 19200

List of positive integer factors of 19200 that divides 19180 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 256, 300, 320, 384, 400, 480, 600, 640, 768, 800, 960, 1200, 1280, 1600, 1920, 2400, 3200, 3840, 4800, 6400, 9600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19180 and 19200. The biggest common factor number is the GCF number.
So the greatest common factor 19180 and 19200 is 20.

Also check out the Least Common Multiple of 19180 and 19200