What is the Greatest Common Factor of 69120 and 69140?

Greatest common factor (GCF) of 69120 and 69140 is 20.

GCF(69120,69140) = 20

We will now calculate the prime factors of 69120 and 69140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69120 and 69140.

How to find the GCF of 69120 and 69140?

We will first find the prime factorization of 69120 and 69140. After we will calculate the factors of 69120 and 69140 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 69140

Prime factors of 69140 are 2, 5, 3457. Prime factorization of 69140 in exponential form is:

69140 = 2² × 5¹ × 3457¹

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 69140

List of positive integer factors of 69140 that divides 69120 without a remainder.

1, 2, 4, 5, 10, 20, 3457, 6914, 13828, 17285, 34570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69120 and 69140. The biggest common factor number is the GCF number.
So the greatest common factor 69120 and 69140 is 20.

Also check out the Least Common Multiple of 69120 and 69140