What is the Greatest Common Factor of 40305 and 40320?

Greatest common factor (GCF) of 40305 and 40320 is 15.

GCF(40305,40320) = 15

We will now calculate the prime factors of 40305 and 40320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 40305 and 40320.

How to find the GCF of 40305 and 40320?

We will first find the prime factorization of 40305 and 40320. After we will calculate the factors of 40305 and 40320 and find the biggest common factor number .

Step-1: Prime Factorization of 40305

Prime factors of 40305 are 3, 5, 2687. Prime factorization of 40305 in exponential form is:

40305 = 3¹ × 5¹ × 2687¹

Step-2: Prime Factorization of 40320

Prime factors of 40320 are 2, 3, 5, 7. Prime factorization of 40320 in exponential form is:

40320 = 2⁷ × 3² × 5¹ × 7¹

Step-3: Factors of 40305

List of positive integer factors of 40305 that divides 40305 without a remainder.

1, 3, 5, 15, 2687, 8061, 13435

Step-4: Factors of 40320

List of positive integer factors of 40320 that divides 40305 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 128, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 384, 420, 448, 480, 504, 560, 576, 630, 640, 672, 720, 840, 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520, 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 40305 and 40320. The biggest common factor number is the GCF number.
So the greatest common factor 40305 and 40320 is 15.

Also check out the Least Common Multiple of 40305 and 40320