What is the Greatest Common Factor of 58800 and 58814?

Greatest common factor (GCF) of 58800 and 58814 is 14.

GCF(58800,58814) = 14

We will now calculate the prime factors of 58800 and 58814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58800 and 58814.

How to find the GCF of 58800 and 58814?

We will first find the prime factorization of 58800 and 58814. After we will calculate the factors of 58800 and 58814 and find the biggest common factor number .

Step-1: Prime Factorization of 58800

Prime factors of 58800 are 2, 3, 5, 7. Prime factorization of 58800 in exponential form is:

58800 = 2⁴ × 3¹ × 5² × 7²

Step-2: Prime Factorization of 58814

Prime factors of 58814 are 2, 7, 4201. Prime factorization of 58814 in exponential form is:

58814 = 2¹ × 7¹ × 4201¹

Step-3: Factors of 58800

List of positive integer factors of 58800 that divides 58800 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 49, 50, 56, 60, 70, 75, 80, 84, 98, 100, 105, 112, 120, 140, 147, 150, 168, 175, 196, 200, 210, 240, 245, 280, 294, 300, 336, 350, 392, 400, 420, 490, 525, 560, 588, 600, 700, 735, 784, 840, 980, 1050, 1176, 1200, 1225, 1400, 1470, 1680, 1960, 2100, 2352, 2450, 2800, 2940, 3675, 3920, 4200, 4900, 5880, 7350, 8400, 9800, 11760, 14700, 19600, 29400

Step-4: Factors of 58814

List of positive integer factors of 58814 that divides 58800 without a remainder.

1, 2, 7, 14, 4201, 8402, 29407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58800 and 58814. The biggest common factor number is the GCF number.
So the greatest common factor 58800 and 58814 is 14.

Also check out the Least Common Multiple of 58800 and 58814