What is the Greatest Common Factor of 82208 and 82222?

Greatest common factor (GCF) of 82208 and 82222 is 14.

GCF(82208,82222) = 14

We will now calculate the prime factors of 82208 and 82222, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82208 and 82222.

How to find the GCF of 82208 and 82222?

We will first find the prime factorization of 82208 and 82222. After we will calculate the factors of 82208 and 82222 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 82222

Prime factors of 82222 are 2, 7, 839. Prime factorization of 82222 in exponential form is:

82222 = 2¹ × 7² × 839¹

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 82222

List of positive integer factors of 82222 that divides 82208 without a remainder.

1, 2, 7, 14, 49, 98, 839, 1678, 5873, 11746, 41111

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82208 and 82222. The biggest common factor number is the GCF number.
So the greatest common factor 82208 and 82222 is 14.

Also check out the Least Common Multiple of 82208 and 82222