What is the Greatest Common Factor of 95985 and 96000?

Greatest common factor (GCF) of 95985 and 96000 is 15.

GCF(95985,96000) = 15

We will now calculate the prime factors of 95985 and 96000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 95985 and 96000.

How to find the GCF of 95985 and 96000?

We will first find the prime factorization of 95985 and 96000. After we will calculate the factors of 95985 and 96000 and find the biggest common factor number .

Step-1: Prime Factorization of 95985

Prime factors of 95985 are 3, 5, 79. Prime factorization of 95985 in exponential form is:

95985 = 3⁵ × 5¹ × 79¹

Step-2: Prime Factorization of 96000

Prime factors of 96000 are 2, 3, 5. Prime factorization of 96000 in exponential form is:

96000 = 2⁸ × 3¹ × 5³

Step-3: Factors of 95985

List of positive integer factors of 95985 that divides 95985 without a remainder.

1, 3, 5, 9, 15, 27, 45, 79, 81, 135, 237, 243, 395, 405, 711, 1185, 1215, 2133, 3555, 6399, 10665, 19197, 31995

Step-4: Factors of 96000

List of positive integer factors of 96000 that divides 95985 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, 125, 128, 150, 160, 192, 200, 240, 250, 256, 300, 320, 375, 384, 400, 480, 500, 600, 640, 750, 768, 800, 960, 1000, 1200, 1280, 1500, 1600, 1920, 2000, 2400, 3000, 3200, 3840, 4000, 4800, 6000, 6400, 8000, 9600, 12000, 16000, 19200, 24000, 32000, 48000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 95985 and 96000. The biggest common factor number is the GCF number.
So the greatest common factor 95985 and 96000 is 15.

Also check out the Least Common Multiple of 95985 and 96000