What is the Greatest Common Factor of 82008 and 82025?

Greatest common factor (GCF) of 82008 and 82025 is 17.

GCF(82008,82025) = 17

We will now calculate the prime factors of 82008 and 82025, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82008 and 82025.

How to find the GCF of 82008 and 82025?

We will first find the prime factorization of 82008 and 82025. After we will calculate the factors of 82008 and 82025 and find the biggest common factor number .

Step-1: Prime Factorization of 82008

Prime factors of 82008 are 2, 3, 17, 67. Prime factorization of 82008 in exponential form is:

82008 = 2³ × 3² × 17¹ × 67¹

Step-2: Prime Factorization of 82025

Prime factors of 82025 are 5, 17, 193. Prime factorization of 82025 in exponential form is:

82025 = 5² × 17¹ × 193¹

Step-3: Factors of 82008

List of positive integer factors of 82008 that divides 82008 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 67, 68, 72, 102, 134, 136, 153, 201, 204, 268, 306, 402, 408, 536, 603, 612, 804, 1139, 1206, 1224, 1608, 2278, 2412, 3417, 4556, 4824, 6834, 9112, 10251, 13668, 20502, 27336, 41004

Step-4: Factors of 82025

List of positive integer factors of 82025 that divides 82008 without a remainder.

1, 5, 17, 25, 85, 193, 425, 965, 3281, 4825, 16405

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82008 and 82025. The biggest common factor number is the GCF number.
So the greatest common factor 82008 and 82025 is 17.

Also check out the Least Common Multiple of 82008 and 82025