What is the Greatest Common Factor of 30705 and 30710?

Greatest common factor (GCF) of 30705 and 30710 is 5.

GCF(30705,30710) = 5

We will now calculate the prime factors of 30705 and 30710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30705 and 30710.

How to find the GCF of 30705 and 30710?

We will first find the prime factorization of 30705 and 30710. After we will calculate the factors of 30705 and 30710 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 30710

Prime factors of 30710 are 2, 5, 37, 83. Prime factorization of 30710 in exponential form is:

30710 = 2¹ × 5¹ × 37¹ × 83¹

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 30710

List of positive integer factors of 30710 that divides 30705 without a remainder.

1, 2, 5, 10, 37, 74, 83, 166, 185, 370, 415, 830, 3071, 6142, 15355

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30705 and 30710. The biggest common factor number is the GCF number.
So the greatest common factor 30705 and 30710 is 5.

Also check out the Least Common Multiple of 30705 and 30710