What is the Greatest Common Factor of 26205 and 26214?

Greatest common factor (GCF) of 26205 and 26214 is 3.

GCF(26205,26214) = 3

We will now calculate the prime factors of 26205 and 26214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26205 and 26214.

How to find the GCF of 26205 and 26214?

We will first find the prime factorization of 26205 and 26214. After we will calculate the factors of 26205 and 26214 and find the biggest common factor number .

Step-1: Prime Factorization of 26205

Prime factors of 26205 are 3, 5, 1747. Prime factorization of 26205 in exponential form is:

26205 = 3¹ × 5¹ × 1747¹

Step-2: Prime Factorization of 26214

Prime factors of 26214 are 2, 3, 17, 257. Prime factorization of 26214 in exponential form is:

26214 = 2¹ × 3¹ × 17¹ × 257¹

Step-3: Factors of 26205

List of positive integer factors of 26205 that divides 26205 without a remainder.

1, 3, 5, 15, 1747, 5241, 8735

Step-4: Factors of 26214

List of positive integer factors of 26214 that divides 26205 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 257, 514, 771, 1542, 4369, 8738, 13107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26205 and 26214. The biggest common factor number is the GCF number.
So the greatest common factor 26205 and 26214 is 3.

Also check out the Least Common Multiple of 26205 and 26214