What is the Greatest Common Factor of 68194 and 68208?

Greatest common factor (GCF) of 68194 and 68208 is 14.

GCF(68194,68208) = 14

We will now calculate the prime factors of 68194 and 68208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 68194 and 68208.

How to find the GCF of 68194 and 68208?

We will first find the prime factorization of 68194 and 68208. After we will calculate the factors of 68194 and 68208 and find the biggest common factor number .

Step-1: Prime Factorization of 68194

Prime factors of 68194 are 2, 7, 4871. Prime factorization of 68194 in exponential form is:

68194 = 2¹ × 7¹ × 4871¹

Step-2: Prime Factorization of 68208

Prime factors of 68208 are 2, 3, 7, 29. Prime factorization of 68208 in exponential form is:

68208 = 2⁴ × 3¹ × 7² × 29¹

Step-3: Factors of 68194

List of positive integer factors of 68194 that divides 68194 without a remainder.

1, 2, 7, 14, 4871, 9742, 34097

Step-4: Factors of 68208

List of positive integer factors of 68208 that divides 68194 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 42, 48, 49, 56, 58, 84, 87, 98, 112, 116, 147, 168, 174, 196, 203, 232, 294, 336, 348, 392, 406, 464, 588, 609, 696, 784, 812, 1176, 1218, 1392, 1421, 1624, 2352, 2436, 2842, 3248, 4263, 4872, 5684, 8526, 9744, 11368, 17052, 22736, 34104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 68194 and 68208. The biggest common factor number is the GCF number.
So the greatest common factor 68194 and 68208 is 14.

Also check out the Least Common Multiple of 68194 and 68208