What is the Greatest Common Factor of 34542 and 34560?

Greatest common factor (GCF) of 34542 and 34560 is 18.

GCF(34542,34560) = 18

We will now calculate the prime factors of 34542 and 34560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34542 and 34560.

How to find the GCF of 34542 and 34560?

We will first find the prime factorization of 34542 and 34560. After we will calculate the factors of 34542 and 34560 and find the biggest common factor number .

Step-1: Prime Factorization of 34542

Prime factors of 34542 are 2, 3, 19, 101. Prime factorization of 34542 in exponential form is:

34542 = 2¹ × 3² × 19¹ × 101¹

Step-2: 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-3: Factors of 34542

List of positive integer factors of 34542 that divides 34542 without a remainder.

1, 2, 3, 6, 9, 18, 19, 38, 57, 101, 114, 171, 202, 303, 342, 606, 909, 1818, 1919, 3838, 5757, 11514, 17271

Step-4: Factors of 34560

List of positive integer factors of 34560 that divides 34542 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34542 and 34560. The biggest common factor number is the GCF number.
So the greatest common factor 34542 and 34560 is 18.

Also check out the Least Common Multiple of 34542 and 34560