What is the Greatest Common Factor of 34560 and 34575?

Greatest common factor (GCF) of 34560 and 34575 is 15.

GCF(34560,34575) = 15

We will now calculate the prime factors of 34560 and 34575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34560 and 34575.

How to find the GCF of 34560 and 34575?

We will first find the prime factorization of 34560 and 34575. After we will calculate the factors of 34560 and 34575 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 34575

Prime factors of 34575 are 3, 5, 461. Prime factorization of 34575 in exponential form is:

34575 = 3¹ × 5² × 461¹

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 34575

List of positive integer factors of 34575 that divides 34560 without a remainder.

1, 3, 5, 15, 25, 75, 461, 1383, 2305, 6915, 11525

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34560 and 34575. The biggest common factor number is the GCF number.
So the greatest common factor 34560 and 34575 is 15.

Also check out the Least Common Multiple of 34560 and 34575