What is the Greatest Common Factor of 25750 and 25770?

Greatest common factor (GCF) of 25750 and 25770 is 10.

GCF(25750,25770) = 10

We will now calculate the prime factors of 25750 and 25770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25750 and 25770.

How to find the GCF of 25750 and 25770?

We will first find the prime factorization of 25750 and 25770. After we will calculate the factors of 25750 and 25770 and find the biggest common factor number .

Step-1: Prime Factorization of 25750

Prime factors of 25750 are 2, 5, 103. Prime factorization of 25750 in exponential form is:

25750 = 2¹ × 5³ × 103¹

Step-2: Prime Factorization of 25770

Prime factors of 25770 are 2, 3, 5, 859. Prime factorization of 25770 in exponential form is:

25770 = 2¹ × 3¹ × 5¹ × 859¹

Step-3: Factors of 25750

List of positive integer factors of 25750 that divides 25750 without a remainder.

1, 2, 5, 10, 25, 50, 103, 125, 206, 250, 515, 1030, 2575, 5150, 12875

Step-4: Factors of 25770

List of positive integer factors of 25770 that divides 25750 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 859, 1718, 2577, 4295, 5154, 8590, 12885

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25750 and 25770. The biggest common factor number is the GCF number.
So the greatest common factor 25750 and 25770 is 10.

Also check out the Least Common Multiple of 25750 and 25770