What is the Greatest Common Factor of 74800 and 74820?

Greatest common factor (GCF) of 74800 and 74820 is 20.

GCF(74800,74820) = 20

We will now calculate the prime factors of 74800 and 74820, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74800 and 74820.

How to find the GCF of 74800 and 74820?

We will first find the prime factorization of 74800 and 74820. After we will calculate the factors of 74800 and 74820 and find the biggest common factor number .

Step-1: Prime Factorization of 74800

Prime factors of 74800 are 2, 5, 11, 17. Prime factorization of 74800 in exponential form is:

74800 = 2⁴ × 5² × 11¹ × 17¹

Step-2: Prime Factorization of 74820

Prime factors of 74820 are 2, 3, 5, 29, 43. Prime factorization of 74820 in exponential form is:

74820 = 2² × 3¹ × 5¹ × 29¹ × 43¹

Step-3: Factors of 74800

List of positive integer factors of 74800 that divides 74800 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 17, 20, 22, 25, 34, 40, 44, 50, 55, 68, 80, 85, 88, 100, 110, 136, 170, 176, 187, 200, 220, 272, 275, 340, 374, 400, 425, 440, 550, 680, 748, 850, 880, 935, 1100, 1360, 1496, 1700, 1870, 2200, 2992, 3400, 3740, 4400, 4675, 6800, 7480, 9350, 14960, 18700, 37400

Step-4: Factors of 74820

List of positive integer factors of 74820 that divides 74800 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 43, 58, 60, 86, 87, 116, 129, 145, 172, 174, 215, 258, 290, 348, 430, 435, 516, 580, 645, 860, 870, 1247, 1290, 1740, 2494, 2580, 3741, 4988, 6235, 7482, 12470, 14964, 18705, 24940, 37410

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74800 and 74820. The biggest common factor number is the GCF number.
So the greatest common factor 74800 and 74820 is 20.

Also check out the Least Common Multiple of 74800 and 74820