What is the Greatest Common Factor of 34560 and 34570?

Greatest common factor (GCF) of 34560 and 34570 is 10.

GCF(34560,34570) = 10

We will now calculate the prime factors of 34560 and 34570, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34560 and 34570.

How to find the GCF of 34560 and 34570?

We will first find the prime factorization of 34560 and 34570. After we will calculate the factors of 34560 and 34570 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 34570

Prime factors of 34570 are 2, 5, 3457. Prime factorization of 34570 in exponential form is:

34570 = 2¹ × 5¹ × 3457¹

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 34570

List of positive integer factors of 34570 that divides 34560 without a remainder.

1, 2, 5, 10, 3457, 6914, 17285

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34560 and 34570. The biggest common factor number is the GCF number.
So the greatest common factor 34560 and 34570 is 10.

Also check out the Least Common Multiple of 34560 and 34570