What is the Greatest Common Factor of 30705 and 30714?

Greatest common factor (GCF) of 30705 and 30714 is 3.

GCF(30705,30714) = 3

We will now calculate the prime factors of 30705 and 30714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30705 and 30714.

How to find the GCF of 30705 and 30714?

We will first find the prime factorization of 30705 and 30714. After we will calculate the factors of 30705 and 30714 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 30714

Prime factors of 30714 are 2, 3, 5119. Prime factorization of 30714 in exponential form is:

30714 = 2¹ × 3¹ × 5119¹

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 30714

List of positive integer factors of 30714 that divides 30705 without a remainder.

1, 2, 3, 6, 5119, 10238, 15357

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30705 and 30714. The biggest common factor number is the GCF number.
So the greatest common factor 30705 and 30714 is 3.

Also check out the Least Common Multiple of 30705 and 30714