What is the Greatest Common Factor of 58800 and 58820?

Greatest common factor (GCF) of 58800 and 58820 is 20.

GCF(58800,58820) = 20

We will now calculate the prime factors of 58800 and 58820, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58800 and 58820.

How to find the GCF of 58800 and 58820?

We will first find the prime factorization of 58800 and 58820. After we will calculate the factors of 58800 and 58820 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 58820

Prime factors of 58820 are 2, 5, 17, 173. Prime factorization of 58820 in exponential form is:

58820 = 2² × 5¹ × 17¹ × 173¹

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 58820

List of positive integer factors of 58820 that divides 58800 without a remainder.

1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 173, 340, 346, 692, 865, 1730, 2941, 3460, 5882, 11764, 14705, 29410

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58800 and 58820. The biggest common factor number is the GCF number.
So the greatest common factor 58800 and 58820 is 20.

Also check out the Least Common Multiple of 58800 and 58820