What is the Greatest Common Factor of 82100 and 82110?

Greatest common factor (GCF) of 82100 and 82110 is 10.

GCF(82100,82110) = 10

We will now calculate the prime factors of 82100 and 82110, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82100 and 82110.

How to find the GCF of 82100 and 82110?

We will first find the prime factorization of 82100 and 82110. After we will calculate the factors of 82100 and 82110 and find the biggest common factor number .

Step-1: Prime Factorization of 82100

Prime factors of 82100 are 2, 5, 821. Prime factorization of 82100 in exponential form is:

82100 = 2² × 5² × 821¹

Step-2: Prime Factorization of 82110

Prime factors of 82110 are 2, 3, 5, 7, 17, 23. Prime factorization of 82110 in exponential form is:

82110 = 2¹ × 3¹ × 5¹ × 7¹ × 17¹ × 23¹

Step-3: Factors of 82100

List of positive integer factors of 82100 that divides 82100 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 821, 1642, 3284, 4105, 8210, 16420, 20525, 41050

Step-4: Factors of 82110

List of positive integer factors of 82110 that divides 82100 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 17, 21, 23, 30, 34, 35, 42, 46, 51, 69, 70, 85, 102, 105, 115, 119, 138, 161, 170, 210, 230, 238, 255, 322, 345, 357, 391, 483, 510, 595, 690, 714, 782, 805, 966, 1173, 1190, 1610, 1785, 1955, 2346, 2415, 2737, 3570, 3910, 4830, 5474, 5865, 8211, 11730, 13685, 16422, 27370, 41055

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82100 and 82110. The biggest common factor number is the GCF number.
So the greatest common factor 82100 and 82110 is 10.

Also check out the Least Common Multiple of 82100 and 82110