What is the Greatest Common Factor of 69120 and 69135?

Greatest common factor (GCF) of 69120 and 69135 is 15.

GCF(69120,69135) = 15

We will now calculate the prime factors of 69120 and 69135, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69120 and 69135.

How to find the GCF of 69120 and 69135?

We will first find the prime factorization of 69120 and 69135. After we will calculate the factors of 69120 and 69135 and find the biggest common factor number .

Step-1: Prime Factorization of 69120

Prime factors of 69120 are 2, 3, 5. Prime factorization of 69120 in exponential form is:

69120 = 2⁹ × 3³ × 5¹

Step-2: Prime Factorization of 69135

Prime factors of 69135 are 3, 5, 11, 419. Prime factorization of 69135 in exponential form is:

69135 = 3¹ × 5¹ × 11¹ × 419¹

Step-3: Factors of 69120

List of positive integer factors of 69120 that divides 69120 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, 512, 540, 576, 640, 720, 768, 864, 960, 1080, 1152, 1280, 1440, 1536, 1728, 1920, 2160, 2304, 2560, 2880, 3456, 3840, 4320, 4608, 5760, 6912, 7680, 8640, 11520, 13824, 17280, 23040, 34560

Step-4: Factors of 69135

List of positive integer factors of 69135 that divides 69120 without a remainder.

1, 3, 5, 11, 15, 33, 55, 165, 419, 1257, 2095, 4609, 6285, 13827, 23045

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69120 and 69135. The biggest common factor number is the GCF number.
So the greatest common factor 69120 and 69135 is 15.

Also check out the Least Common Multiple of 69120 and 69135