What is the Greatest Common Factor of 82000 and 82010?

Greatest common factor (GCF) of 82000 and 82010 is 10.

GCF(82000,82010) = 10

We will now calculate the prime factors of 82000 and 82010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82000 and 82010.

How to find the GCF of 82000 and 82010?

We will first find the prime factorization of 82000 and 82010. After we will calculate the factors of 82000 and 82010 and find the biggest common factor number .

Step-1: Prime Factorization of 82000

Prime factors of 82000 are 2, 5, 41. Prime factorization of 82000 in exponential form is:

82000 = 2⁴ × 5³ × 41¹

Step-2: Prime Factorization of 82010

Prime factors of 82010 are 2, 5, 59, 139. Prime factorization of 82010 in exponential form is:

82010 = 2¹ × 5¹ × 59¹ × 139¹

Step-3: Factors of 82000

List of positive integer factors of 82000 that divides 82000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 41, 50, 80, 82, 100, 125, 164, 200, 205, 250, 328, 400, 410, 500, 656, 820, 1000, 1025, 1640, 2000, 2050, 3280, 4100, 5125, 8200, 10250, 16400, 20500, 41000

Step-4: Factors of 82010

List of positive integer factors of 82010 that divides 82000 without a remainder.

1, 2, 5, 10, 59, 118, 139, 278, 295, 590, 695, 1390, 8201, 16402, 41005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82000 and 82010. The biggest common factor number is the GCF number.
So the greatest common factor 82000 and 82010 is 10.

Also check out the Least Common Multiple of 82000 and 82010