What is the Greatest Common Factor of 16000 and 16014?

Greatest common factor (GCF) of 16000 and 16014 is 2.

GCF(16000,16014) = 2

We will now calculate the prime factors of 16000 and 16014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16000 and 16014.

How to find the GCF of 16000 and 16014?

We will first find the prime factorization of 16000 and 16014. After we will calculate the factors of 16000 and 16014 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 16014

Prime factors of 16014 are 2, 3, 17, 157. Prime factorization of 16014 in exponential form is:

16014 = 2¹ × 3¹ × 17¹ × 157¹

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 16014

List of positive integer factors of 16014 that divides 16000 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 157, 314, 471, 942, 2669, 5338, 8007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16000 and 16014. The biggest common factor number is the GCF number.
So the greatest common factor 16000 and 16014 is 2.

Also check out the Least Common Multiple of 16000 and 16014