What is the Greatest Common Factor of 32000 and 32010?

Greatest common factor (GCF) of 32000 and 32010 is 10.

GCF(32000,32010) = 10

We will now calculate the prime factors of 32000 and 32010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32000 and 32010.

How to find the GCF of 32000 and 32010?

We will first find the prime factorization of 32000 and 32010. After we will calculate the factors of 32000 and 32010 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 32010

Prime factors of 32010 are 2, 3, 5, 11, 97. Prime factorization of 32010 in exponential form is:

32010 = 2¹ × 3¹ × 5¹ × 11¹ × 97¹

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 32010

List of positive integer factors of 32010 that divides 32000 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 97, 110, 165, 194, 291, 330, 485, 582, 970, 1067, 1455, 2134, 2910, 3201, 5335, 6402, 10670, 16005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32000 and 32010. The biggest common factor number is the GCF number.
So the greatest common factor 32000 and 32010 is 10.

Also check out the Least Common Multiple of 32000 and 32010