What is the Greatest Common Factor of 10234 and 10250?

Greatest common factor (GCF) of 10234 and 10250 is 2.

GCF(10234,10250) = 2

We will now calculate the prime factors of 10234 and 10250, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10234 and 10250.

How to find the GCF of 10234 and 10250?

We will first find the prime factorization of 10234 and 10250. After we will calculate the factors of 10234 and 10250 and find the biggest common factor number .

Step-1: Prime Factorization of 10234

Prime factors of 10234 are 2, 7, 17, 43. Prime factorization of 10234 in exponential form is:

10234 = 2¹ × 7¹ × 17¹ × 43¹

Step-2: 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-3: Factors of 10234

List of positive integer factors of 10234 that divides 10234 without a remainder.

1, 2, 7, 14, 17, 34, 43, 86, 119, 238, 301, 602, 731, 1462, 5117

Step-4: Factors of 10250

List of positive integer factors of 10250 that divides 10234 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10234 and 10250. The biggest common factor number is the GCF number.
So the greatest common factor 10234 and 10250 is 2.

Also check out the Least Common Multiple of 10234 and 10250