What is the Greatest Common Factor of 32000 and 32008?

Greatest common factor (GCF) of 32000 and 32008 is 8.

GCF(32000,32008) = 8

We will now calculate the prime factors of 32000 and 32008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32000 and 32008.

How to find the GCF of 32000 and 32008?

We will first find the prime factorization of 32000 and 32008. After we will calculate the factors of 32000 and 32008 and find the biggest common factor number .

Step-1: Prime Factorization of 32000

Prime factors of 32000 are 2, 5. Prime factorization of 32000 in exponential form is:

32000 = 2⁸ × 5³

Step-2: Prime Factorization of 32008

Prime factors of 32008 are 2, 4001. Prime factorization of 32008 in exponential form is:

32008 = 2³ × 4001¹

Step-3: Factors of 32000

List of positive integer factors of 32000 that divides 32000 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, 640, 800, 1000, 1280, 1600, 2000, 3200, 4000, 6400, 8000, 16000

Step-4: Factors of 32008

List of positive integer factors of 32008 that divides 32000 without a remainder.

1, 2, 4, 8, 4001, 8002, 16004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32000 and 32008. The biggest common factor number is the GCF number.
So the greatest common factor 32000 and 32008 is 8.

Also check out the Least Common Multiple of 32000 and 32008