What is the Greatest Common Factor of 10257 and 10275?

Greatest common factor (GCF) of 10257 and 10275 is 3.

GCF(10257,10275) = 3

We will now calculate the prime factors of 10257 and 10275, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10257 and 10275.

How to find the GCF of 10257 and 10275?

We will first find the prime factorization of 10257 and 10275. After we will calculate the factors of 10257 and 10275 and find the biggest common factor number .

Step-1: Prime Factorization of 10257

Prime factors of 10257 are 3, 13, 263. Prime factorization of 10257 in exponential form is:

10257 = 3¹ × 13¹ × 263¹

Step-2: Prime Factorization of 10275

Prime factors of 10275 are 3, 5, 137. Prime factorization of 10275 in exponential form is:

10275 = 3¹ × 5² × 137¹

Step-3: Factors of 10257

List of positive integer factors of 10257 that divides 10257 without a remainder.

1, 3, 13, 39, 263, 789, 3419

Step-4: Factors of 10275

List of positive integer factors of 10275 that divides 10257 without a remainder.

1, 3, 5, 15, 25, 75, 137, 411, 685, 2055, 3425

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10257 and 10275. The biggest common factor number is the GCF number.
So the greatest common factor 10257 and 10275 is 3.

Also check out the Least Common Multiple of 10257 and 10275