What is the Greatest Common Factor of 82980 and 83000?

Greatest common factor (GCF) of 82980 and 83000 is 20.

GCF(82980,83000) = 20

We will now calculate the prime factors of 82980 and 83000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82980 and 83000.

How to find the GCF of 82980 and 83000?

We will first find the prime factorization of 82980 and 83000. After we will calculate the factors of 82980 and 83000 and find the biggest common factor number .

Step-1: Prime Factorization of 82980

Prime factors of 82980 are 2, 3, 5, 461. Prime factorization of 82980 in exponential form is:

82980 = 2² × 3² × 5¹ × 461¹

Step-2: Prime Factorization of 83000

Prime factors of 83000 are 2, 5, 83. Prime factorization of 83000 in exponential form is:

83000 = 2³ × 5³ × 83¹

Step-3: Factors of 82980

List of positive integer factors of 82980 that divides 82980 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 461, 922, 1383, 1844, 2305, 2766, 4149, 4610, 5532, 6915, 8298, 9220, 13830, 16596, 20745, 27660, 41490

Step-4: Factors of 83000

List of positive integer factors of 83000 that divides 82980 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 83, 100, 125, 166, 200, 250, 332, 415, 500, 664, 830, 1000, 1660, 2075, 3320, 4150, 8300, 10375, 16600, 20750, 41500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82980 and 83000. The biggest common factor number is the GCF number.
So the greatest common factor 82980 and 83000 is 20.

Also check out the Least Common Multiple of 82980 and 83000