What is the Greatest Common Factor of 10250 and 10260?

Greatest common factor (GCF) of 10250 and 10260 is 10.

GCF(10250,10260) = 10

We will now calculate the prime factors of 10250 and 10260, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10250 and 10260.

How to find the GCF of 10250 and 10260?

We will first find the prime factorization of 10250 and 10260. After we will calculate the factors of 10250 and 10260 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 10260

Prime factors of 10260 are 2, 3, 5, 19. Prime factorization of 10260 in exponential form is:

10260 = 2² × 3³ × 5¹ × 19¹

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 10260

List of positive integer factors of 10260 that divides 10250 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 27, 30, 36, 38, 45, 54, 57, 60, 76, 90, 95, 108, 114, 135, 171, 180, 190, 228, 270, 285, 342, 380, 513, 540, 570, 684, 855, 1026, 1140, 1710, 2052, 2565, 3420, 5130

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10250 and 10260. The biggest common factor number is the GCF number.
So the greatest common factor 10250 and 10260 is 10.

Also check out the Least Common Multiple of 10250 and 10260