What is the Greatest Common Factor of 64000 and 64005?

Greatest common factor (GCF) of 64000 and 64005 is 5.

GCF(64000,64005) = 5

We will now calculate the prime factors of 64000 and 64005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 64000 and 64005.

How to find the GCF of 64000 and 64005?

We will first find the prime factorization of 64000 and 64005. After we will calculate the factors of 64000 and 64005 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 64005

Prime factors of 64005 are 3, 5, 17, 251. Prime factorization of 64005 in exponential form is:

64005 = 3¹ × 5¹ × 17¹ × 251¹

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 64005

List of positive integer factors of 64005 that divides 64000 without a remainder.

1, 3, 5, 15, 17, 51, 85, 251, 255, 753, 1255, 3765, 4267, 12801, 21335

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 64000 and 64005. The biggest common factor number is the GCF number.
So the greatest common factor 64000 and 64005 is 5.

Also check out the Least Common Multiple of 64000 and 64005