What is the Greatest Common Factor of 34560 and 34576?

Greatest common factor (GCF) of 34560 and 34576 is 16.

GCF(34560,34576) = 16

We will now calculate the prime factors of 34560 and 34576, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34560 and 34576.

How to find the GCF of 34560 and 34576?

We will first find the prime factorization of 34560 and 34576. After we will calculate the factors of 34560 and 34576 and find the biggest common factor number .

Step-1: Prime Factorization of 34560

Prime factors of 34560 are 2, 3, 5. Prime factorization of 34560 in exponential form is:

34560 = 2⁸ × 3³ × 5¹

Step-2: Prime Factorization of 34576

Prime factors of 34576 are 2, 2161. Prime factorization of 34576 in exponential form is:

34576 = 2⁴ × 2161¹

Step-3: Factors of 34560

List of positive integer factors of 34560 that divides 34560 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 90, 96, 108, 120, 128, 135, 144, 160, 180, 192, 216, 240, 256, 270, 288, 320, 360, 384, 432, 480, 540, 576, 640, 720, 768, 864, 960, 1080, 1152, 1280, 1440, 1728, 1920, 2160, 2304, 2880, 3456, 3840, 4320, 5760, 6912, 8640, 11520, 17280

Step-4: Factors of 34576

List of positive integer factors of 34576 that divides 34560 without a remainder.

1, 2, 4, 8, 16, 2161, 4322, 8644, 17288

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34560 and 34576. The biggest common factor number is the GCF number.
So the greatest common factor 34560 and 34576 is 16.

Also check out the Least Common Multiple of 34560 and 34576