What is the Greatest Common Factor of 74783 and 74800?

Greatest common factor (GCF) of 74783 and 74800 is 17.

GCF(74783,74800) = 17

We will now calculate the prime factors of 74783 and 74800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74783 and 74800.

How to find the GCF of 74783 and 74800?

We will first find the prime factorization of 74783 and 74800. After we will calculate the factors of 74783 and 74800 and find the biggest common factor number .

Step-1: Prime Factorization of 74783

Prime factors of 74783 are 17, 53, 83. Prime factorization of 74783 in exponential form is:

74783 = 17¹ × 53¹ × 83¹

Step-2: 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-3: Factors of 74783

List of positive integer factors of 74783 that divides 74783 without a remainder.

1, 17, 53, 83, 901, 1411, 4399

Step-4: Factors of 74800

List of positive integer factors of 74800 that divides 74783 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74783 and 74800. The biggest common factor number is the GCF number.
So the greatest common factor 74783 and 74800 is 17.

Also check out the Least Common Multiple of 74783 and 74800