What is the Greatest Common Factor of 78705 and 78720?

Greatest common factor (GCF) of 78705 and 78720 is 15.

GCF(78705,78720) = 15

We will now calculate the prime factors of 78705 and 78720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78705 and 78720.

How to find the GCF of 78705 and 78720?

We will first find the prime factorization of 78705 and 78720. After we will calculate the factors of 78705 and 78720 and find the biggest common factor number .

Step-1: Prime Factorization of 78705

Prime factors of 78705 are 3, 5, 11, 53. Prime factorization of 78705 in exponential form is:

78705 = 3³ × 5¹ × 11¹ × 53¹

Step-2: Prime Factorization of 78720

Prime factors of 78720 are 2, 3, 5, 41. Prime factorization of 78720 in exponential form is:

78720 = 2⁷ × 3¹ × 5¹ × 41¹

Step-3: Factors of 78705

List of positive integer factors of 78705 that divides 78705 without a remainder.

1, 3, 5, 9, 11, 15, 27, 33, 45, 53, 55, 99, 135, 159, 165, 265, 297, 477, 495, 583, 795, 1431, 1485, 1749, 2385, 2915, 5247, 7155, 8745, 15741, 26235

Step-4: Factors of 78720

List of positive integer factors of 78720 that divides 78705 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 41, 48, 60, 64, 80, 82, 96, 120, 123, 128, 160, 164, 192, 205, 240, 246, 320, 328, 384, 410, 480, 492, 615, 640, 656, 820, 960, 984, 1230, 1312, 1640, 1920, 1968, 2460, 2624, 3280, 3936, 4920, 5248, 6560, 7872, 9840, 13120, 15744, 19680, 26240, 39360

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78705 and 78720. The biggest common factor number is the GCF number.
So the greatest common factor 78705 and 78720 is 15.

Also check out the Least Common Multiple of 78705 and 78720