What is the Greatest Common Factor of 13125 and 13138?

Greatest common factor (GCF) of 13125 and 13138 is 1.

GCF(13125,13138) = 1

We will now calculate the prime factors of 13125 and 13138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13125 and 13138.

How to find the GCF of 13125 and 13138?

We will first find the prime factorization of 13125 and 13138. After we will calculate the factors of 13125 and 13138 and find the biggest common factor number .

Step-1: Prime Factorization of 13125

Prime factors of 13125 are 3, 5, 7. Prime factorization of 13125 in exponential form is:

13125 = 3¹ × 5⁴ × 7¹

Step-2: Prime Factorization of 13138

Prime factors of 13138 are 2, 6569. Prime factorization of 13138 in exponential form is:

13138 = 2¹ × 6569¹

Step-3: Factors of 13125

List of positive integer factors of 13125 that divides 13125 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 625, 875, 1875, 2625, 4375

Step-4: Factors of 13138

List of positive integer factors of 13138 that divides 13125 without a remainder.

1, 2, 6569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13125 and 13138. The biggest common factor number is the GCF number.
So the greatest common factor 13125 and 13138 is 1.

Also check out the Least Common Multiple of 13125 and 13138