What is the Greatest Common Factor of 16000 and 16005?

Greatest common factor (GCF) of 16000 and 16005 is 5.

GCF(16000,16005) = 5

We will now calculate the prime factors of 16000 and 16005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16000 and 16005.

How to find the GCF of 16000 and 16005?

We will first find the prime factorization of 16000 and 16005. After we will calculate the factors of 16000 and 16005 and find the biggest common factor number .

Step-1: Prime Factorization of 16000

Prime factors of 16000 are 2, 5. Prime factorization of 16000 in exponential form is:

16000 = 2⁷ × 5³

Step-2: Prime Factorization of 16005

Prime factors of 16005 are 3, 5, 11, 97. Prime factorization of 16005 in exponential form is:

16005 = 3¹ × 5¹ × 11¹ × 97¹

Step-3: Factors of 16000

List of positive integer factors of 16000 that divides 16000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 320, 400, 500, 640, 800, 1000, 1600, 2000, 3200, 4000, 8000

Step-4: Factors of 16005

List of positive integer factors of 16005 that divides 16000 without a remainder.

1, 3, 5, 11, 15, 33, 55, 97, 165, 291, 485, 1067, 1455, 3201, 5335

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16000 and 16005. The biggest common factor number is the GCF number.
So the greatest common factor 16000 and 16005 is 5.

Also check out the Least Common Multiple of 16000 and 16005