What is the Greatest Common Factor of 78720 and 78735?

Greatest common factor (GCF) of 78720 and 78735 is 15.

GCF(78720,78735) = 15

We will now calculate the prime factors of 78720 and 78735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78720 and 78735.

How to find the GCF of 78720 and 78735?

We will first find the prime factorization of 78720 and 78735. After we will calculate the factors of 78720 and 78735 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 78735

Prime factors of 78735 are 3, 5, 29, 181. Prime factorization of 78735 in exponential form is:

78735 = 3¹ × 5¹ × 29¹ × 181¹

Step-3: Factors of 78720

List of positive integer factors of 78720 that divides 78720 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

Step-4: Factors of 78735

List of positive integer factors of 78735 that divides 78720 without a remainder.

1, 3, 5, 15, 29, 87, 145, 181, 435, 543, 905, 2715, 5249, 15747, 26245

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78720 and 78735. The biggest common factor number is the GCF number.
So the greatest common factor 78720 and 78735 is 15.

Also check out the Least Common Multiple of 78720 and 78735