What is the Greatest Common Factor of 34560 and 34569?

Greatest common factor (GCF) of 34560 and 34569 is 9.

GCF(34560,34569) = 9

We will now calculate the prime factors of 34560 and 34569, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34560 and 34569.

How to find the GCF of 34560 and 34569?

We will first find the prime factorization of 34560 and 34569. After we will calculate the factors of 34560 and 34569 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 34569

Prime factors of 34569 are 3, 23, 167. Prime factorization of 34569 in exponential form is:

34569 = 3² × 23¹ × 167¹

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 34569

List of positive integer factors of 34569 that divides 34560 without a remainder.

1, 3, 9, 23, 69, 167, 207, 501, 1503, 3841, 11523

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34560 and 34569. The biggest common factor number is the GCF number.
So the greatest common factor 34560 and 34569 is 9.

Also check out the Least Common Multiple of 34560 and 34569