What is the Greatest Common Factor of 74867 and 74880?

Greatest common factor (GCF) of 74867 and 74880 is 13.

GCF(74867,74880) = 13

We will now calculate the prime factors of 74867 and 74880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74867 and 74880.

How to find the GCF of 74867 and 74880?

We will first find the prime factorization of 74867 and 74880. After we will calculate the factors of 74867 and 74880 and find the biggest common factor number .

Step-1: Prime Factorization of 74867

Prime factors of 74867 are 13, 443. Prime factorization of 74867 in exponential form is:

74867 = 13² × 443¹

Step-2: Prime Factorization of 74880

Prime factors of 74880 are 2, 3, 5, 13. Prime factorization of 74880 in exponential form is:

74880 = 2⁷ × 3² × 5¹ × 13¹

Step-3: Factors of 74867

List of positive integer factors of 74867 that divides 74867 without a remainder.

1, 13, 169, 443, 5759

Step-4: Factors of 74880

List of positive integer factors of 74880 that divides 74867 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24, 26, 30, 32, 36, 39, 40, 45, 48, 52, 60, 64, 65, 72, 78, 80, 90, 96, 104, 117, 120, 128, 130, 144, 156, 160, 180, 192, 195, 208, 234, 240, 260, 288, 312, 320, 360, 384, 390, 416, 468, 480, 520, 576, 585, 624, 640, 720, 780, 832, 936, 960, 1040, 1152, 1170, 1248, 1440, 1560, 1664, 1872, 1920, 2080, 2340, 2496, 2880, 3120, 3744, 4160, 4680, 4992, 5760, 6240, 7488, 8320, 9360, 12480, 14976, 18720, 24960, 37440

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74867 and 74880. The biggest common factor number is the GCF number.
So the greatest common factor 74867 and 74880 is 13.

Also check out the Least Common Multiple of 74867 and 74880