What is the Greatest Common Factor of 5730 and 5750?

Greatest common factor (GCF) of 5730 and 5750 is 10.

GCF(5730,5750) = 10

We will now calculate the prime factors of 5730 and 5750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5730 and 5750.

How to find the GCF of 5730 and 5750?

We will first find the prime factorization of 5730 and 5750. After we will calculate the factors of 5730 and 5750 and find the biggest common factor number .

Step-1: Prime Factorization of 5730

Prime factors of 5730 are 2, 3, 5, 191. Prime factorization of 5730 in exponential form is:

5730 = 2¹ × 3¹ × 5¹ × 191¹

Step-2: Prime Factorization of 5750

Prime factors of 5750 are 2, 5, 23. Prime factorization of 5750 in exponential form is:

5750 = 2¹ × 5³ × 23¹

Step-3: Factors of 5730

List of positive integer factors of 5730 that divides 5730 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 191, 382, 573, 955, 1146, 1910, 2865

Step-4: Factors of 5750

List of positive integer factors of 5750 that divides 5730 without a remainder.

1, 2, 5, 10, 23, 25, 46, 50, 115, 125, 230, 250, 575, 1150, 2875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5730 and 5750. The biggest common factor number is the GCF number.
So the greatest common factor 5730 and 5750 is 10.

Also check out the Least Common Multiple of 5730 and 5750