What is the Greatest Common Factor of 34560 and 34578?

Greatest common factor (GCF) of 34560 and 34578 is 18.

GCF(34560,34578) = 18

We will now calculate the prime factors of 34560 and 34578, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34560 and 34578.

How to find the GCF of 34560 and 34578?

We will first find the prime factorization of 34560 and 34578. After we will calculate the factors of 34560 and 34578 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 34578

Prime factors of 34578 are 2, 3, 17, 113. Prime factorization of 34578 in exponential form is:

34578 = 2¹ × 3² × 17¹ × 113¹

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 34578

List of positive integer factors of 34578 that divides 34560 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 113, 153, 226, 306, 339, 678, 1017, 1921, 2034, 3842, 5763, 11526, 17289

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34560 and 34578. The biggest common factor number is the GCF number.
So the greatest common factor 34560 and 34578 is 18.

Also check out the Least Common Multiple of 34560 and 34578