What is the Greatest Common Factor of 12814 and 12825?

Greatest common factor (GCF) of 12814 and 12825 is 1.

GCF(12814,12825) = 1

We will now calculate the prime factors of 12814 and 12825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12814 and 12825.

How to find the GCF of 12814 and 12825?

We will first find the prime factorization of 12814 and 12825. After we will calculate the factors of 12814 and 12825 and find the biggest common factor number .

Step-1: Prime Factorization of 12814

Prime factors of 12814 are 2, 43, 149. Prime factorization of 12814 in exponential form is:

12814 = 2¹ × 43¹ × 149¹

Step-2: Prime Factorization of 12825

Prime factors of 12825 are 3, 5, 19. Prime factorization of 12825 in exponential form is:

12825 = 3³ × 5² × 19¹

Step-3: Factors of 12814

List of positive integer factors of 12814 that divides 12814 without a remainder.

1, 2, 43, 86, 149, 298, 6407

Step-4: Factors of 12825

List of positive integer factors of 12825 that divides 12814 without a remainder.

1, 3, 5, 9, 15, 19, 25, 27, 45, 57, 75, 95, 135, 171, 225, 285, 475, 513, 675, 855, 1425, 2565, 4275

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12814 and 12825. The biggest common factor number is the GCF number.
So the greatest common factor 12814 and 12825 is 1.

Also check out the Least Common Multiple of 12814 and 12825