What is the Greatest Common Factor of 13286 and 13300?

Greatest common factor (GCF) of 13286 and 13300 is 14.

GCF(13286,13300) = 14

We will now calculate the prime factors of 13286 and 13300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13286 and 13300.

How to find the GCF of 13286 and 13300?

We will first find the prime factorization of 13286 and 13300. After we will calculate the factors of 13286 and 13300 and find the biggest common factor number .

Step-1: Prime Factorization of 13286

Prime factors of 13286 are 2, 7, 13, 73. Prime factorization of 13286 in exponential form is:

13286 = 2¹ × 7¹ × 13¹ × 73¹

Step-2: Prime Factorization of 13300

Prime factors of 13300 are 2, 5, 7, 19. Prime factorization of 13300 in exponential form is:

13300 = 2² × 5² × 7¹ × 19¹

Step-3: Factors of 13286

List of positive integer factors of 13286 that divides 13286 without a remainder.

1, 2, 7, 13, 14, 26, 73, 91, 146, 182, 511, 949, 1022, 1898, 6643

Step-4: Factors of 13300

List of positive integer factors of 13300 that divides 13286 without a remainder.

1, 2, 4, 5, 7, 10, 14, 19, 20, 25, 28, 35, 38, 50, 70, 76, 95, 100, 133, 140, 175, 190, 266, 350, 380, 475, 532, 665, 700, 950, 1330, 1900, 2660, 3325, 6650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13286 and 13300. The biggest common factor number is the GCF number.
So the greatest common factor 13286 and 13300 is 14.

Also check out the Least Common Multiple of 13286 and 13300