What is the Greatest Common Factor of 64000 and 64008?

Greatest common factor (GCF) of 64000 and 64008 is 8.

GCF(64000,64008) = 8

We will now calculate the prime factors of 64000 and 64008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 64000 and 64008.

How to find the GCF of 64000 and 64008?

We will first find the prime factorization of 64000 and 64008. After we will calculate the factors of 64000 and 64008 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 64008

Prime factors of 64008 are 2, 3, 7, 127. Prime factorization of 64008 in exponential form is:

64008 = 2³ × 3² × 7¹ × 127¹

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 64008

List of positive integer factors of 64008 that divides 64000 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 127, 168, 252, 254, 381, 504, 508, 762, 889, 1016, 1143, 1524, 1778, 2286, 2667, 3048, 3556, 4572, 5334, 7112, 8001, 9144, 10668, 16002, 21336, 32004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 64000 and 64008. The biggest common factor number is the GCF number.
So the greatest common factor 64000 and 64008 is 8.

Also check out the Least Common Multiple of 64000 and 64008