What is the Greatest Common Factor of 74800 and 74817?

Greatest common factor (GCF) of 74800 and 74817 is 17.

GCF(74800,74817) = 17

We will now calculate the prime factors of 74800 and 74817, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74800 and 74817.

How to find the GCF of 74800 and 74817?

We will first find the prime factorization of 74800 and 74817. After we will calculate the factors of 74800 and 74817 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 74817

Prime factors of 74817 are 3, 17, 163. Prime factorization of 74817 in exponential form is:

74817 = 3³ × 17¹ × 163¹

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 74817

List of positive integer factors of 74817 that divides 74800 without a remainder.

1, 3, 9, 17, 27, 51, 153, 163, 459, 489, 1467, 2771, 4401, 8313, 24939

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74800 and 74817. The biggest common factor number is the GCF number.
So the greatest common factor 74800 and 74817 is 17.

Also check out the Least Common Multiple of 74800 and 74817