What is the Greatest Common Factor of 30735 and 30750?

Greatest common factor (GCF) of 30735 and 30750 is 15.

GCF(30735,30750) = 15

We will now calculate the prime factors of 30735 and 30750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30735 and 30750.

How to find the GCF of 30735 and 30750?

We will first find the prime factorization of 30735 and 30750. After we will calculate the factors of 30735 and 30750 and find the biggest common factor number .

Step-1: Prime Factorization of 30735

Prime factors of 30735 are 3, 5, 683. Prime factorization of 30735 in exponential form is:

30735 = 3² × 5¹ × 683¹

Step-2: Prime Factorization of 30750

Prime factors of 30750 are 2, 3, 5, 41. Prime factorization of 30750 in exponential form is:

30750 = 2¹ × 3¹ × 5³ × 41¹

Step-3: Factors of 30735

List of positive integer factors of 30735 that divides 30735 without a remainder.

1, 3, 5, 9, 15, 45, 683, 2049, 3415, 6147, 10245

Step-4: Factors of 30750

List of positive integer factors of 30750 that divides 30735 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 41, 50, 75, 82, 123, 125, 150, 205, 246, 250, 375, 410, 615, 750, 1025, 1230, 2050, 3075, 5125, 6150, 10250, 15375

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30735 and 30750. The biggest common factor number is the GCF number.
So the greatest common factor 30735 and 30750 is 15.

Also check out the Least Common Multiple of 30735 and 30750