What is the Greatest Common Factor of 65584 and 65600?

Greatest common factor (GCF) of 65584 and 65600 is 16.

GCF(65584,65600) = 16

We will now calculate the prime factors of 65584 and 65600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65584 and 65600.

How to find the GCF of 65584 and 65600?

We will first find the prime factorization of 65584 and 65600. After we will calculate the factors of 65584 and 65600 and find the biggest common factor number .

Step-1: Prime Factorization of 65584

Prime factors of 65584 are 2, 4099. Prime factorization of 65584 in exponential form is:

65584 = 2⁴ × 4099¹

Step-2: Prime Factorization of 65600

Prime factors of 65600 are 2, 5, 41. Prime factorization of 65600 in exponential form is:

65600 = 2⁶ × 5² × 41¹

Step-3: Factors of 65584

List of positive integer factors of 65584 that divides 65584 without a remainder.

1, 2, 4, 8, 16, 4099, 8198, 16396, 32792

Step-4: Factors of 65600

List of positive integer factors of 65600 that divides 65584 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 41, 50, 64, 80, 82, 100, 160, 164, 200, 205, 320, 328, 400, 410, 656, 800, 820, 1025, 1312, 1600, 1640, 2050, 2624, 3280, 4100, 6560, 8200, 13120, 16400, 32800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65584 and 65600. The biggest common factor number is the GCF number.
So the greatest common factor 65584 and 65600 is 16.

Also check out the Least Common Multiple of 65584 and 65600