What is the Greatest Common Factor of 30705 and 30712?

Greatest common factor (GCF) of 30705 and 30712 is 1.

GCF(30705,30712) = 1

We will now calculate the prime factors of 30705 and 30712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30705 and 30712.

How to find the GCF of 30705 and 30712?

We will first find the prime factorization of 30705 and 30712. After we will calculate the factors of 30705 and 30712 and find the biggest common factor number .

Step-1: 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-2: 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-3: Factors of 30705

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

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

Step-4: Factors of 30712

List of positive integer factors of 30712 that divides 30705 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30705 and 30712. The biggest common factor number is the GCF number.
So the greatest common factor 30705 and 30712 is 1.

Also check out the Least Common Multiple of 30705 and 30712