What is the Greatest Common Factor of 30696 and 30702?

Greatest common factor (GCF) of 30696 and 30702 is 6.

GCF(30696,30702) = 6

We will now calculate the prime factors of 30696 and 30702, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30696 and 30702.

How to find the GCF of 30696 and 30702?

We will first find the prime factorization of 30696 and 30702. After we will calculate the factors of 30696 and 30702 and find the biggest common factor number .

Step-1: Prime Factorization of 30696

Prime factors of 30696 are 2, 3, 1279. Prime factorization of 30696 in exponential form is:

30696 = 2³ × 3¹ × 1279¹

Step-2: Prime Factorization of 30702

Prime factors of 30702 are 2, 3, 7, 17, 43. Prime factorization of 30702 in exponential form is:

30702 = 2¹ × 3¹ × 7¹ × 17¹ × 43¹

Step-3: Factors of 30696

List of positive integer factors of 30696 that divides 30696 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1279, 2558, 3837, 5116, 7674, 10232, 15348

Step-4: Factors of 30702

List of positive integer factors of 30702 that divides 30696 without a remainder.

1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 43, 51, 86, 102, 119, 129, 238, 258, 301, 357, 602, 714, 731, 903, 1462, 1806, 2193, 4386, 5117, 10234, 15351

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30696 and 30702. The biggest common factor number is the GCF number.
So the greatest common factor 30696 and 30702 is 6.

Also check out the Least Common Multiple of 30696 and 30702