What is the Greatest Common Factor of 72786 and 72800?

Greatest common factor (GCF) of 72786 and 72800 is 14.

GCF(72786,72800) = 14

We will now calculate the prime factors of 72786 and 72800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72786 and 72800.

How to find the GCF of 72786 and 72800?

We will first find the prime factorization of 72786 and 72800. After we will calculate the factors of 72786 and 72800 and find the biggest common factor number .

Step-1: Prime Factorization of 72786

Prime factors of 72786 are 2, 3, 7, 1733. Prime factorization of 72786 in exponential form is:

72786 = 2¹ × 3¹ × 7¹ × 1733¹

Step-2: 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-3: Factors of 72786

List of positive integer factors of 72786 that divides 72786 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1733, 3466, 5199, 10398, 12131, 24262, 36393

Step-4: Factors of 72800

List of positive integer factors of 72800 that divides 72786 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72786 and 72800. The biggest common factor number is the GCF number.
So the greatest common factor 72786 and 72800 is 14.

Also check out the Least Common Multiple of 72786 and 72800