What is the Greatest Common Factor of 10730 and 10750?

Greatest common factor (GCF) of 10730 and 10750 is 10.

GCF(10730,10750) = 10

We will now calculate the prime factors of 10730 and 10750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10730 and 10750.

How to find the GCF of 10730 and 10750?

We will first find the prime factorization of 10730 and 10750. After we will calculate the factors of 10730 and 10750 and find the biggest common factor number .

Step-1: Prime Factorization of 10730

Prime factors of 10730 are 2, 5, 29, 37. Prime factorization of 10730 in exponential form is:

10730 = 2¹ × 5¹ × 29¹ × 37¹

Step-2: 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-3: Factors of 10730

List of positive integer factors of 10730 that divides 10730 without a remainder.

1, 2, 5, 10, 29, 37, 58, 74, 145, 185, 290, 370, 1073, 2146, 5365

Step-4: Factors of 10750

List of positive integer factors of 10750 that divides 10730 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10730 and 10750. The biggest common factor number is the GCF number.
So the greatest common factor 10730 and 10750 is 10.

Also check out the Least Common Multiple of 10730 and 10750