What is the Greatest Common Factor of 64000 and 64014?

Greatest common factor (GCF) of 64000 and 64014 is 2.

GCF(64000,64014) = 2

We will now calculate the prime factors of 64000 and 64014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 64000 and 64014.

How to find the GCF of 64000 and 64014?

We will first find the prime factorization of 64000 and 64014. After we will calculate the factors of 64000 and 64014 and find the biggest common factor number .

Step-1: Prime Factorization of 64000

Prime factors of 64000 are 2, 5. Prime factorization of 64000 in exponential form is:

64000 = 2⁹ × 5³

Step-2: Prime Factorization of 64014

Prime factors of 64014 are 2, 3, 47, 227. Prime factorization of 64014 in exponential form is:

64014 = 2¹ × 3¹ × 47¹ × 227¹

Step-3: Factors of 64000

List of positive integer factors of 64000 that divides 64000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 640, 800, 1000, 1280, 1600, 2000, 2560, 3200, 4000, 6400, 8000, 12800, 16000, 32000

Step-4: Factors of 64014

List of positive integer factors of 64014 that divides 64000 without a remainder.

1, 2, 3, 6, 47, 94, 141, 227, 282, 454, 681, 1362, 10669, 21338, 32007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 64000 and 64014. The biggest common factor number is the GCF number.
So the greatest common factor 64000 and 64014 is 2.

Also check out the Least Common Multiple of 64000 and 64014