What is the Greatest Common Factor of 31993 and 32000?

Greatest common factor (GCF) of 31993 and 32000 is 1.

GCF(31993,32000) = 1

We will now calculate the prime factors of 31993 and 32000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31993 and 32000.

How to find the GCF of 31993 and 32000?

We will first find the prime factorization of 31993 and 32000. After we will calculate the factors of 31993 and 32000 and find the biggest common factor number .

Step-1: Prime Factorization of 31993

Prime factors of 31993 are 13, 23, 107. Prime factorization of 31993 in exponential form is:

31993 = 13¹ × 23¹ × 107¹

Step-2: Prime Factorization of 32000

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

32000 = 2⁸ × 5³

Step-3: Factors of 31993

List of positive integer factors of 31993 that divides 31993 without a remainder.

1, 13, 23, 107, 299, 1391, 2461

Step-4: Factors of 32000

List of positive integer factors of 32000 that divides 31993 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31993 and 32000. The biggest common factor number is the GCF number.
So the greatest common factor 31993 and 32000 is 1.

Also check out the Least Common Multiple of 31993 and 32000