What is the Greatest Common Factor of 58800 and 58812?

Greatest common factor (GCF) of 58800 and 58812 is 12.

GCF(58800,58812) = 12

We will now calculate the prime factors of 58800 and 58812, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58800 and 58812.

How to find the GCF of 58800 and 58812?

We will first find the prime factorization of 58800 and 58812. After we will calculate the factors of 58800 and 58812 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 58812

Prime factors of 58812 are 2, 3, 13, 29. Prime factorization of 58812 in exponential form is:

58812 = 2² × 3¹ × 13² × 29¹

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 58812

List of positive integer factors of 58812 that divides 58800 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 29, 39, 52, 58, 78, 87, 116, 156, 169, 174, 338, 348, 377, 507, 676, 754, 1014, 1131, 1508, 2028, 2262, 4524, 4901, 9802, 14703, 19604, 29406

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58800 and 58812. The biggest common factor number is the GCF number.
So the greatest common factor 58800 and 58812 is 12.

Also check out the Least Common Multiple of 58800 and 58812