What is the Greatest Common Factor of 69105 and 69120?

Greatest common factor (GCF) of 69105 and 69120 is 15.

GCF(69105,69120) = 15

We will now calculate the prime factors of 69105 and 69120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69105 and 69120.

How to find the GCF of 69105 and 69120?

We will first find the prime factorization of 69105 and 69120. After we will calculate the factors of 69105 and 69120 and find the biggest common factor number .

Step-1: Prime Factorization of 69105

Prime factors of 69105 are 3, 5, 17, 271. Prime factorization of 69105 in exponential form is:

69105 = 3¹ × 5¹ × 17¹ × 271¹

Step-2: 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-3: Factors of 69105

List of positive integer factors of 69105 that divides 69105 without a remainder.

1, 3, 5, 15, 17, 51, 85, 255, 271, 813, 1355, 4065, 4607, 13821, 23035

Step-4: Factors of 69120

List of positive integer factors of 69120 that divides 69105 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69105 and 69120. The biggest common factor number is the GCF number.
So the greatest common factor 69105 and 69120 is 15.

Also check out the Least Common Multiple of 69105 and 69120