What is the Greatest Common Factor of 30723 and 30742?

Greatest common factor (GCF) of 30723 and 30742 is 19.

GCF(30723,30742) = 19

We will now calculate the prime factors of 30723 and 30742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30723 and 30742.

How to find the GCF of 30723 and 30742?

We will first find the prime factorization of 30723 and 30742. After we will calculate the factors of 30723 and 30742 and find the biggest common factor number .

Step-1: Prime Factorization of 30723

Prime factors of 30723 are 3, 7, 11, 19. Prime factorization of 30723 in exponential form is:

30723 = 3¹ × 7² × 11¹ × 19¹

Step-2: Prime Factorization of 30742

Prime factors of 30742 are 2, 19, 809. Prime factorization of 30742 in exponential form is:

30742 = 2¹ × 19¹ × 809¹

Step-3: Factors of 30723

List of positive integer factors of 30723 that divides 30723 without a remainder.

1, 3, 7, 11, 19, 21, 33, 49, 57, 77, 133, 147, 209, 231, 399, 539, 627, 931, 1463, 1617, 2793, 4389, 10241

Step-4: Factors of 30742

List of positive integer factors of 30742 that divides 30723 without a remainder.

1, 2, 19, 38, 809, 1618, 15371

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30723 and 30742. The biggest common factor number is the GCF number.
So the greatest common factor 30723 and 30742 is 19.

Also check out the Least Common Multiple of 30723 and 30742