What is the Greatest Common Factor of 74800 and 74816?

Greatest common factor (GCF) of 74800 and 74816 is 16.

GCF(74800,74816) = 16

We will now calculate the prime factors of 74800 and 74816, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74800 and 74816.

How to find the GCF of 74800 and 74816?

We will first find the prime factorization of 74800 and 74816. After we will calculate the factors of 74800 and 74816 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 74816

Prime factors of 74816 are 2, 7, 167. Prime factorization of 74816 in exponential form is:

74816 = 2⁶ × 7¹ × 167¹

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 74816

List of positive integer factors of 74816 that divides 74800 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 167, 224, 334, 448, 668, 1169, 1336, 2338, 2672, 4676, 5344, 9352, 10688, 18704, 37408

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74800 and 74816. The biggest common factor number is the GCF number.
So the greatest common factor 74800 and 74816 is 16.

Also check out the Least Common Multiple of 74800 and 74816