What is the Greatest Common Factor of 82208 and 82215?

Greatest common factor (GCF) of 82208 and 82215 is 7.

GCF(82208,82215) = 7

We will now calculate the prime factors of 82208 and 82215, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82208 and 82215.

How to find the GCF of 82208 and 82215?

We will first find the prime factorization of 82208 and 82215. After we will calculate the factors of 82208 and 82215 and find the biggest common factor number .

Step-1: Prime Factorization of 82208

Prime factors of 82208 are 2, 7, 367. Prime factorization of 82208 in exponential form is:

82208 = 2⁵ × 7¹ × 367¹

Step-2: Prime Factorization of 82215

Prime factors of 82215 are 3, 5, 7, 29. Prime factorization of 82215 in exponential form is:

82215 = 3⁴ × 5¹ × 7¹ × 29¹

Step-3: Factors of 82208

List of positive integer factors of 82208 that divides 82208 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224, 367, 734, 1468, 2569, 2936, 5138, 5872, 10276, 11744, 20552, 41104

Step-4: Factors of 82215

List of positive integer factors of 82215 that divides 82208 without a remainder.

1, 3, 5, 7, 9, 15, 21, 27, 29, 35, 45, 63, 81, 87, 105, 135, 145, 189, 203, 261, 315, 405, 435, 567, 609, 783, 945, 1015, 1305, 1827, 2349, 2835, 3045, 3915, 5481, 9135, 11745, 16443, 27405

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82208 and 82215. The biggest common factor number is the GCF number.
So the greatest common factor 82208 and 82215 is 7.

Also check out the Least Common Multiple of 82208 and 82215