What is the Greatest Common Factor of 34560 and 34565?

Greatest common factor (GCF) of 34560 and 34565 is 5.

GCF(34560,34565) = 5

We will now calculate the prime factors of 34560 and 34565, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34560 and 34565.

How to find the GCF of 34560 and 34565?

We will first find the prime factorization of 34560 and 34565. After we will calculate the factors of 34560 and 34565 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 34565

Prime factors of 34565 are 5, 31, 223. Prime factorization of 34565 in exponential form is:

34565 = 5¹ × 31¹ × 223¹

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 34565

List of positive integer factors of 34565 that divides 34560 without a remainder.

1, 5, 31, 155, 223, 1115, 6913

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34560 and 34565. The biggest common factor number is the GCF number.
So the greatest common factor 34560 and 34565 is 5.

Also check out the Least Common Multiple of 34560 and 34565