What is the Greatest Common Factor of 16000 and 16009?

Greatest common factor (GCF) of 16000 and 16009 is 1.

GCF(16000,16009) = 1

We will now calculate the prime factors of 16000 and 16009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16000 and 16009.

How to find the GCF of 16000 and 16009?

We will first find the prime factorization of 16000 and 16009. After we will calculate the factors of 16000 and 16009 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 16009

Prime factors of 16009 are 7, 2287. Prime factorization of 16009 in exponential form is:

16009 = 7¹ × 2287¹

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 16009

List of positive integer factors of 16009 that divides 16000 without a remainder.

1, 7, 2287

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16000 and 16009. The biggest common factor number is the GCF number.
So the greatest common factor 16000 and 16009 is 1.

Also check out the Least Common Multiple of 16000 and 16009