What is the Greatest Common Factor of 6000 and 6016?

Greatest common factor (GCF) of 6000 and 6016 is 16.

GCF(6000,6016) = 16

We will now calculate the prime factors of 6000 and 6016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6000 and 6016.

How to find the GCF of 6000 and 6016?

We will first find the prime factorization of 6000 and 6016. After we will calculate the factors of 6000 and 6016 and find the biggest common factor number .

Step-1: Prime Factorization of 6000

Prime factors of 6000 are 2, 3, 5. Prime factorization of 6000 in exponential form is:

6000 = 2⁴ × 3¹ × 5³

Step-2: Prime Factorization of 6016

Prime factors of 6016 are 2, 47. Prime factorization of 6016 in exponential form is:

6016 = 2⁷ × 47¹

Step-3: Factors of 6000

List of positive integer factors of 6000 that divides 6000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000

Step-4: Factors of 6016

List of positive integer factors of 6016 that divides 6000 without a remainder.

1, 2, 4, 8, 16, 32, 47, 64, 94, 128, 188, 376, 752, 1504, 3008

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6000 and 6016. The biggest common factor number is the GCF number.
So the greatest common factor 6000 and 6016 is 16.

Also check out the Least Common Multiple of 6000 and 6016