What is the Greatest Common Factor of 10250 and 10270?

Greatest common factor (GCF) of 10250 and 10270 is 10.

GCF(10250,10270) = 10

We will now calculate the prime factors of 10250 and 10270, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10250 and 10270.

How to find the GCF of 10250 and 10270?

We will first find the prime factorization of 10250 and 10270. After we will calculate the factors of 10250 and 10270 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 10270

Prime factors of 10270 are 2, 5, 13, 79. Prime factorization of 10270 in exponential form is:

10270 = 2¹ × 5¹ × 13¹ × 79¹

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 10270

List of positive integer factors of 10270 that divides 10250 without a remainder.

1, 2, 5, 10, 13, 26, 65, 79, 130, 158, 395, 790, 1027, 2054, 5135

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10250 and 10270. The biggest common factor number is the GCF number.
So the greatest common factor 10250 and 10270 is 10.

Also check out the Least Common Multiple of 10250 and 10270