What is the Greatest Common Factor of 82000 and 82004?

Greatest common factor (GCF) of 82000 and 82004 is 4.

GCF(82000,82004) = 4

We will now calculate the prime factors of 82000 and 82004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82000 and 82004.

How to find the GCF of 82000 and 82004?

We will first find the prime factorization of 82000 and 82004. After we will calculate the factors of 82000 and 82004 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 82004

Prime factors of 82004 are 2, 13, 19, 83. Prime factorization of 82004 in exponential form is:

82004 = 2² × 13¹ × 19¹ × 83¹

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 82004

List of positive integer factors of 82004 that divides 82000 without a remainder.

1, 2, 4, 13, 19, 26, 38, 52, 76, 83, 166, 247, 332, 494, 988, 1079, 1577, 2158, 3154, 4316, 6308, 20501, 41002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82000 and 82004. The biggest common factor number is the GCF number.
So the greatest common factor 82000 and 82004 is 4.

Also check out the Least Common Multiple of 82000 and 82004