What is the Greatest Common Factor of 14875 and 14889?

Greatest common factor (GCF) of 14875 and 14889 is 7.

GCF(14875,14889) = 7

We will now calculate the prime factors of 14875 and 14889, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14875 and 14889.

How to find the GCF of 14875 and 14889?

We will first find the prime factorization of 14875 and 14889. After we will calculate the factors of 14875 and 14889 and find the biggest common factor number .

Step-1: Prime Factorization of 14875

Prime factors of 14875 are 5, 7, 17. Prime factorization of 14875 in exponential form is:

14875 = 5³ × 7¹ × 17¹

Step-2: Prime Factorization of 14889

Prime factors of 14889 are 3, 7, 709. Prime factorization of 14889 in exponential form is:

14889 = 3¹ × 7¹ × 709¹

Step-3: Factors of 14875

List of positive integer factors of 14875 that divides 14875 without a remainder.

1, 5, 7, 17, 25, 35, 85, 119, 125, 175, 425, 595, 875, 2125, 2975

Step-4: Factors of 14889

List of positive integer factors of 14889 that divides 14875 without a remainder.

1, 3, 7, 21, 709, 2127, 4963

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14875 and 14889. The biggest common factor number is the GCF number.
So the greatest common factor 14875 and 14889 is 7.

Also check out the Least Common Multiple of 14875 and 14889