What is the Greatest Common Factor of 96000 and 96014?

Greatest common factor (GCF) of 96000 and 96014 is 2.

GCF(96000,96014) = 2

We will now calculate the prime factors of 96000 and 96014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 96000 and 96014.

How to find the GCF of 96000 and 96014?

We will first find the prime factorization of 96000 and 96014. After we will calculate the factors of 96000 and 96014 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 96014

Prime factors of 96014 are 2, 61, 787. Prime factorization of 96014 in exponential form is:

96014 = 2¹ × 61¹ × 787¹

Step-3: Factors of 96000

List of positive integer factors of 96000 that divides 96000 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

Step-4: Factors of 96014

List of positive integer factors of 96014 that divides 96000 without a remainder.

1, 2, 61, 122, 787, 1574, 48007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 96000 and 96014. The biggest common factor number is the GCF number.
So the greatest common factor 96000 and 96014 is 2.

Also check out the Least Common Multiple of 96000 and 96014