What is the Greatest Common Factor of 30688 and 30696?

Greatest common factor (GCF) of 30688 and 30696 is 8.

GCF(30688,30696) = 8

We will now calculate the prime factors of 30688 and 30696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30688 and 30696.

How to find the GCF of 30688 and 30696?

We will first find the prime factorization of 30688 and 30696. After we will calculate the factors of 30688 and 30696 and find the biggest common factor number .

Step-1: Prime Factorization of 30688

Prime factors of 30688 are 2, 7, 137. Prime factorization of 30688 in exponential form is:

30688 = 2⁵ × 7¹ × 137¹

Step-2: 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-3: Factors of 30688

List of positive integer factors of 30688 that divides 30688 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 137, 224, 274, 548, 959, 1096, 1918, 2192, 3836, 4384, 7672, 15344

Step-4: Factors of 30696

List of positive integer factors of 30696 that divides 30688 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30688 and 30696. The biggest common factor number is the GCF number.
So the greatest common factor 30688 and 30696 is 8.

Also check out the Least Common Multiple of 30688 and 30696