What is the Greatest Common Factor of 30675 and 30690?

Greatest common factor (GCF) of 30675 and 30690 is 15.

GCF(30675,30690) = 15

We will now calculate the prime factors of 30675 and 30690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30675 and 30690.

How to find the GCF of 30675 and 30690?

We will first find the prime factorization of 30675 and 30690. After we will calculate the factors of 30675 and 30690 and find the biggest common factor number .

Step-1: Prime Factorization of 30675

Prime factors of 30675 are 3, 5, 409. Prime factorization of 30675 in exponential form is:

30675 = 3¹ × 5² × 409¹

Step-2: Prime Factorization of 30690

Prime factors of 30690 are 2, 3, 5, 11, 31. Prime factorization of 30690 in exponential form is:

30690 = 2¹ × 3² × 5¹ × 11¹ × 31¹

Step-3: Factors of 30675

List of positive integer factors of 30675 that divides 30675 without a remainder.

1, 3, 5, 15, 25, 75, 409, 1227, 2045, 6135, 10225

Step-4: Factors of 30690

List of positive integer factors of 30690 that divides 30675 without a remainder.

1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 31, 33, 45, 55, 62, 66, 90, 93, 99, 110, 155, 165, 186, 198, 279, 310, 330, 341, 465, 495, 558, 682, 930, 990, 1023, 1395, 1705, 2046, 2790, 3069, 3410, 5115, 6138, 10230, 15345

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30675 and 30690. The biggest common factor number is the GCF number.
So the greatest common factor 30675 and 30690 is 15.

Also check out the Least Common Multiple of 30675 and 30690