What is the Greatest Common Factor of 72800 and 72810?

Greatest common factor (GCF) of 72800 and 72810 is 10.

GCF(72800,72810) = 10

We will now calculate the prime factors of 72800 and 72810, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72800 and 72810.

How to find the GCF of 72800 and 72810?

We will first find the prime factorization of 72800 and 72810. After we will calculate the factors of 72800 and 72810 and find the biggest common factor number .

Step-1: Prime Factorization of 72800

Prime factors of 72800 are 2, 5, 7, 13. Prime factorization of 72800 in exponential form is:

72800 = 2⁵ × 5² × 7¹ × 13¹

Step-2: Prime Factorization of 72810

Prime factors of 72810 are 2, 3, 5, 809. Prime factorization of 72810 in exponential form is:

72810 = 2¹ × 3² × 5¹ × 809¹

Step-3: Factors of 72800

List of positive integer factors of 72800 that divides 72800 without a remainder.

1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 25, 26, 28, 32, 35, 40, 50, 52, 56, 65, 70, 80, 91, 100, 104, 112, 130, 140, 160, 175, 182, 200, 208, 224, 260, 280, 325, 350, 364, 400, 416, 455, 520, 560, 650, 700, 728, 800, 910, 1040, 1120, 1300, 1400, 1456, 1820, 2080, 2275, 2600, 2800, 2912, 3640, 4550, 5200, 5600, 7280, 9100, 10400, 14560, 18200, 36400

Step-4: Factors of 72810

List of positive integer factors of 72810 that divides 72800 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 809, 1618, 2427, 4045, 4854, 7281, 8090, 12135, 14562, 24270, 36405

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72800 and 72810. The biggest common factor number is the GCF number.
So the greatest common factor 72800 and 72810 is 10.

Also check out the Least Common Multiple of 72800 and 72810