What is the Greatest Common Factor of 19275 and 19284?

Greatest common factor (GCF) of 19275 and 19284 is 3.

GCF(19275,19284) = 3

We will now calculate the prime factors of 19275 and 19284, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19275 and 19284.

How to find the GCF of 19275 and 19284?

We will first find the prime factorization of 19275 and 19284. After we will calculate the factors of 19275 and 19284 and find the biggest common factor number .

Step-1: Prime Factorization of 19275

Prime factors of 19275 are 3, 5, 257. Prime factorization of 19275 in exponential form is:

19275 = 3¹ × 5² × 257¹

Step-2: Prime Factorization of 19284

Prime factors of 19284 are 2, 3, 1607. Prime factorization of 19284 in exponential form is:

19284 = 2² × 3¹ × 1607¹

Step-3: Factors of 19275

List of positive integer factors of 19275 that divides 19275 without a remainder.

1, 3, 5, 15, 25, 75, 257, 771, 1285, 3855, 6425

Step-4: Factors of 19284

List of positive integer factors of 19284 that divides 19275 without a remainder.

1, 2, 3, 4, 6, 12, 1607, 3214, 4821, 6428, 9642

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19275 and 19284. The biggest common factor number is the GCF number.
So the greatest common factor 19275 and 19284 is 3.

Also check out the Least Common Multiple of 19275 and 19284