What is the Greatest Common Factor of 26200 and 26214?

Greatest common factor (GCF) of 26200 and 26214 is 2.

GCF(26200,26214) = 2

We will now calculate the prime factors of 26200 and 26214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26200 and 26214.

How to find the GCF of 26200 and 26214?

We will first find the prime factorization of 26200 and 26214. After we will calculate the factors of 26200 and 26214 and find the biggest common factor number .

Step-1: Prime Factorization of 26200

Prime factors of 26200 are 2, 5, 131. Prime factorization of 26200 in exponential form is:

26200 = 2³ × 5² × 131¹

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 26200

List of positive integer factors of 26200 that divides 26200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 131, 200, 262, 524, 655, 1048, 1310, 2620, 3275, 5240, 6550, 13100

Step-4: Factors of 26214

List of positive integer factors of 26214 that divides 26200 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 26200 and 26214. The biggest common factor number is the GCF number.
So the greatest common factor 26200 and 26214 is 2.

Also check out the Least Common Multiple of 26200 and 26214