What is the Greatest Common Factor of 10114 and 10125?

Greatest common factor (GCF) of 10114 and 10125 is 1.

GCF(10114,10125) = 1

We will now calculate the prime factors of 10114 and 10125, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10114 and 10125.

How to find the GCF of 10114 and 10125?

We will first find the prime factorization of 10114 and 10125. After we will calculate the factors of 10114 and 10125 and find the biggest common factor number .

Step-1: Prime Factorization of 10114

Prime factors of 10114 are 2, 13, 389. Prime factorization of 10114 in exponential form is:

10114 = 2¹ × 13¹ × 389¹

Step-2: Prime Factorization of 10125

Prime factors of 10125 are 3, 5. Prime factorization of 10125 in exponential form is:

10125 = 3⁴ × 5³

Step-3: Factors of 10114

List of positive integer factors of 10114 that divides 10114 without a remainder.

1, 2, 13, 26, 389, 778, 5057

Step-4: Factors of 10125

List of positive integer factors of 10125 that divides 10114 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, 375, 405, 675, 1125, 2025, 3375

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10114 and 10125. The biggest common factor number is the GCF number.
So the greatest common factor 10114 and 10125 is 1.

Also check out the Least Common Multiple of 10114 and 10125