What is the Greatest Common Factor of 82208 and 82214?

Greatest common factor (GCF) of 82208 and 82214 is 2.

GCF(82208,82214) = 2

We will now calculate the prime factors of 82208 and 82214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82208 and 82214.

How to find the GCF of 82208 and 82214?

We will first find the prime factorization of 82208 and 82214. After we will calculate the factors of 82208 and 82214 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 82214

Prime factors of 82214 are 2, 11, 37, 101. Prime factorization of 82214 in exponential form is:

82214 = 2¹ × 11¹ × 37¹ × 101¹

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 82214

List of positive integer factors of 82214 that divides 82208 without a remainder.

1, 2, 11, 22, 37, 74, 101, 202, 407, 814, 1111, 2222, 3737, 7474, 41107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82208 and 82214. The biggest common factor number is the GCF number.
So the greatest common factor 82208 and 82214 is 2.

Also check out the Least Common Multiple of 82208 and 82214