What is the Greatest Common Factor of 26194 and 26208?

Greatest common factor (GCF) of 26194 and 26208 is 14.

GCF(26194,26208) = 14

We will now calculate the prime factors of 26194 and 26208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26194 and 26208.

How to find the GCF of 26194 and 26208?

We will first find the prime factorization of 26194 and 26208. After we will calculate the factors of 26194 and 26208 and find the biggest common factor number .

Step-1: Prime Factorization of 26194

Prime factors of 26194 are 2, 7, 1871. Prime factorization of 26194 in exponential form is:

26194 = 2¹ × 7¹ × 1871¹

Step-2: Prime Factorization of 26208

Prime factors of 26208 are 2, 3, 7, 13. Prime factorization of 26208 in exponential form is:

26208 = 2⁵ × 3² × 7¹ × 13¹

Step-3: Factors of 26194

List of positive integer factors of 26194 that divides 26194 without a remainder.

1, 2, 7, 14, 1871, 3742, 13097

Step-4: Factors of 26208

List of positive integer factors of 26208 that divides 26194 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 16, 18, 21, 24, 26, 28, 32, 36, 39, 42, 48, 52, 56, 63, 72, 78, 84, 91, 96, 104, 112, 117, 126, 144, 156, 168, 182, 208, 224, 234, 252, 273, 288, 312, 336, 364, 416, 468, 504, 546, 624, 672, 728, 819, 936, 1008, 1092, 1248, 1456, 1638, 1872, 2016, 2184, 2912, 3276, 3744, 4368, 6552, 8736, 13104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26194 and 26208. The biggest common factor number is the GCF number.
So the greatest common factor 26194 and 26208 is 14.

Also check out the Least Common Multiple of 26194 and 26208