What is the Greatest Common Factor of 30712 and 30723?

Greatest common factor (GCF) of 30712 and 30723 is 11.

GCF(30712,30723) = 11

We will now calculate the prime factors of 30712 and 30723, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30712 and 30723.

How to find the GCF of 30712 and 30723?

We will first find the prime factorization of 30712 and 30723. After we will calculate the factors of 30712 and 30723 and find the biggest common factor number .

Step-1: Prime Factorization of 30712

Prime factors of 30712 are 2, 11, 349. Prime factorization of 30712 in exponential form is:

30712 = 2³ × 11¹ × 349¹

Step-2: 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-3: Factors of 30712

List of positive integer factors of 30712 that divides 30712 without a remainder.

1, 2, 4, 8, 11, 22, 44, 88, 349, 698, 1396, 2792, 3839, 7678, 15356

Step-4: Factors of 30723

List of positive integer factors of 30723 that divides 30712 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30712 and 30723. The biggest common factor number is the GCF number.
So the greatest common factor 30712 and 30723 is 11.

Also check out the Least Common Multiple of 30712 and 30723