What is the Greatest Common Factor of 30690 and 30705?

Greatest common factor (GCF) of 30690 and 30705 is 15.

GCF(30690,30705) = 15

We will now calculate the prime factors of 30690 and 30705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30690 and 30705.

How to find the GCF of 30690 and 30705?

We will first find the prime factorization of 30690 and 30705. After we will calculate the factors of 30690 and 30705 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30705

Prime factors of 30705 are 3, 5, 23, 89. Prime factorization of 30705 in exponential form is:

30705 = 3¹ × 5¹ × 23¹ × 89¹

Step-3: Factors of 30690

List of positive integer factors of 30690 that divides 30690 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

Step-4: Factors of 30705

List of positive integer factors of 30705 that divides 30690 without a remainder.

1, 3, 5, 15, 23, 69, 89, 115, 267, 345, 445, 1335, 2047, 6141, 10235

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30690 and 30705. The biggest common factor number is the GCF number.
So the greatest common factor 30690 and 30705 is 15.

Also check out the Least Common Multiple of 30690 and 30705