What is the Greatest Common Factor of 19565 and 19584?

Greatest common factor (GCF) of 19565 and 19584 is 1.

GCF(19565,19584) = 1

We will now calculate the prime factors of 19565 and 19584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19565 and 19584.

How to find the GCF of 19565 and 19584?

We will first find the prime factorization of 19565 and 19584. After we will calculate the factors of 19565 and 19584 and find the biggest common factor number .

Step-1: Prime Factorization of 19565

Prime factors of 19565 are 5, 7, 13, 43. Prime factorization of 19565 in exponential form is:

19565 = 5¹ × 7¹ × 13¹ × 43¹

Step-2: Prime Factorization of 19584

Prime factors of 19584 are 2, 3, 17. Prime factorization of 19584 in exponential form is:

19584 = 2⁷ × 3² × 17¹

Step-3: Factors of 19565

List of positive integer factors of 19565 that divides 19565 without a remainder.

1, 5, 7, 13, 35, 43, 65, 91, 215, 301, 455, 559, 1505, 2795, 3913

Step-4: Factors of 19584

List of positive integer factors of 19584 that divides 19565 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 32, 34, 36, 48, 51, 64, 68, 72, 96, 102, 128, 136, 144, 153, 192, 204, 272, 288, 306, 384, 408, 544, 576, 612, 816, 1088, 1152, 1224, 1632, 2176, 2448, 3264, 4896, 6528, 9792

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19565 and 19584. The biggest common factor number is the GCF number.
So the greatest common factor 19565 and 19584 is 1.

Also check out the Least Common Multiple of 19565 and 19584