What is the Greatest Common Factor of 58785 and 58800?

Greatest common factor (GCF) of 58785 and 58800 is 15.

GCF(58785,58800) = 15

We will now calculate the prime factors of 58785 and 58800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58785 and 58800.

How to find the GCF of 58785 and 58800?

We will first find the prime factorization of 58785 and 58800. After we will calculate the factors of 58785 and 58800 and find the biggest common factor number .

Step-1: Prime Factorization of 58785

Prime factors of 58785 are 3, 5, 3919. Prime factorization of 58785 in exponential form is:

58785 = 3¹ × 5¹ × 3919¹

Step-2: 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-3: Factors of 58785

List of positive integer factors of 58785 that divides 58785 without a remainder.

1, 3, 5, 15, 3919, 11757, 19595

Step-4: Factors of 58800

List of positive integer factors of 58800 that divides 58785 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58785 and 58800. The biggest common factor number is the GCF number.
So the greatest common factor 58785 and 58800 is 15.

Also check out the Least Common Multiple of 58785 and 58800