What is the Greatest Common Factor of 34560 and 34574?

Greatest common factor (GCF) of 34560 and 34574 is 2.

GCF(34560,34574) = 2

We will now calculate the prime factors of 34560 and 34574, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34560 and 34574.

How to find the GCF of 34560 and 34574?

We will first find the prime factorization of 34560 and 34574. After we will calculate the factors of 34560 and 34574 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 34574

Prime factors of 34574 are 2, 59, 293. Prime factorization of 34574 in exponential form is:

34574 = 2¹ × 59¹ × 293¹

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 34574

List of positive integer factors of 34574 that divides 34560 without a remainder.

1, 2, 59, 118, 293, 586, 17287

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34560 and 34574. The biggest common factor number is the GCF number.
So the greatest common factor 34560 and 34574 is 2.

Also check out the Least Common Multiple of 34560 and 34574