What is the Greatest Common Factor of 10750 and 10770?

Greatest common factor (GCF) of 10750 and 10770 is 10.

GCF(10750,10770) = 10

We will now calculate the prime factors of 10750 and 10770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10750 and 10770.

How to find the GCF of 10750 and 10770?

We will first find the prime factorization of 10750 and 10770. After we will calculate the factors of 10750 and 10770 and find the biggest common factor number .

Step-1: Prime Factorization of 10750

Prime factors of 10750 are 2, 5, 43. Prime factorization of 10750 in exponential form is:

10750 = 2¹ × 5³ × 43¹

Step-2: Prime Factorization of 10770

Prime factors of 10770 are 2, 3, 5, 359. Prime factorization of 10770 in exponential form is:

10770 = 2¹ × 3¹ × 5¹ × 359¹

Step-3: Factors of 10750

List of positive integer factors of 10750 that divides 10750 without a remainder.

1, 2, 5, 10, 25, 43, 50, 86, 125, 215, 250, 430, 1075, 2150, 5375

Step-4: Factors of 10770

List of positive integer factors of 10770 that divides 10750 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 359, 718, 1077, 1795, 2154, 3590, 5385

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10750 and 10770. The biggest common factor number is the GCF number.
So the greatest common factor 10750 and 10770 is 10.

Also check out the Least Common Multiple of 10750 and 10770