What is the Greatest Common Factor of 30670 and 30690?

Greatest common factor (GCF) of 30670 and 30690 is 10.

GCF(30670,30690) = 10

We will now calculate the prime factors of 30670 and 30690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30670 and 30690.

How to find the GCF of 30670 and 30690?

We will first find the prime factorization of 30670 and 30690. After we will calculate the factors of 30670 and 30690 and find the biggest common factor number .

Step-1: Prime Factorization of 30670

Prime factors of 30670 are 2, 5, 3067. Prime factorization of 30670 in exponential form is:

30670 = 2¹ × 5¹ × 3067¹

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 30670

List of positive integer factors of 30670 that divides 30670 without a remainder.

1, 2, 5, 10, 3067, 6134, 15335

Step-4: Factors of 30690

List of positive integer factors of 30690 that divides 30670 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 30670 and 30690. The biggest common factor number is the GCF number.
So the greatest common factor 30670 and 30690 is 10.

Also check out the Least Common Multiple of 30670 and 30690