What is the Greatest Common Factor of 10250 and 10262?

Greatest common factor (GCF) of 10250 and 10262 is 2.

GCF(10250,10262) = 2

We will now calculate the prime factors of 10250 and 10262, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10250 and 10262.

How to find the GCF of 10250 and 10262?

We will first find the prime factorization of 10250 and 10262. After we will calculate the factors of 10250 and 10262 and find the biggest common factor number .

Step-1: Prime Factorization of 10250

Prime factors of 10250 are 2, 5, 41. Prime factorization of 10250 in exponential form is:

10250 = 2¹ × 5³ × 41¹

Step-2: Prime Factorization of 10262

Prime factors of 10262 are 2, 7, 733. Prime factorization of 10262 in exponential form is:

10262 = 2¹ × 7¹ × 733¹

Step-3: Factors of 10250

List of positive integer factors of 10250 that divides 10250 without a remainder.

1, 2, 5, 10, 25, 41, 50, 82, 125, 205, 250, 410, 1025, 2050, 5125

Step-4: Factors of 10262

List of positive integer factors of 10262 that divides 10250 without a remainder.

1, 2, 7, 14, 733, 1466, 5131

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10250 and 10262. The biggest common factor number is the GCF number.
So the greatest common factor 10250 and 10262 is 2.

Also check out the Least Common Multiple of 10250 and 10262