What is the Greatest Common Factor of 30688 and 30700?

Greatest common factor (GCF) of 30688 and 30700 is 4.

GCF(30688,30700) = 4

We will now calculate the prime factors of 30688 and 30700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30688 and 30700.

How to find the GCF of 30688 and 30700?

We will first find the prime factorization of 30688 and 30700. After we will calculate the factors of 30688 and 30700 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 30700

Prime factors of 30700 are 2, 5, 307. Prime factorization of 30700 in exponential form is:

30700 = 2² × 5² × 307¹

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 30700

List of positive integer factors of 30700 that divides 30688 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 307, 614, 1228, 1535, 3070, 6140, 7675, 15350

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30688 and 30700. The biggest common factor number is the GCF number.
So the greatest common factor 30688 and 30700 is 4.

Also check out the Least Common Multiple of 30688 and 30700