What is the Greatest Common Factor of 30688 and 30705?

Greatest common factor (GCF) of 30688 and 30705 is 1.

GCF(30688,30705) = 1

We will now calculate the prime factors of 30688 and 30705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30688 and 30705.

How to find the GCF of 30688 and 30705?

We will first find the prime factorization of 30688 and 30705. After we will calculate the factors of 30688 and 30705 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 30705

Prime factors of 30705 are 3, 5, 23, 89. Prime factorization of 30705 in exponential form is:

30705 = 3¹ × 5¹ × 23¹ × 89¹

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 30705

List of positive integer factors of 30705 that divides 30688 without a remainder.

1, 3, 5, 15, 23, 69, 89, 115, 267, 345, 445, 1335, 2047, 6141, 10235

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30688 and 30705. The biggest common factor number is the GCF number.
So the greatest common factor 30688 and 30705 is 1.

Also check out the Least Common Multiple of 30688 and 30705