What is the Greatest Common Factor of 23664 and 23680?

Greatest common factor (GCF) of 23664 and 23680 is 16.

GCF(23664,23680) = 16

We will now calculate the prime factors of 23664 and 23680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23664 and 23680.

How to find the GCF of 23664 and 23680?

We will first find the prime factorization of 23664 and 23680. After we will calculate the factors of 23664 and 23680 and find the biggest common factor number .

Step-1: Prime Factorization of 23664

Prime factors of 23664 are 2, 3, 17, 29. Prime factorization of 23664 in exponential form is:

23664 = 2⁴ × 3¹ × 17¹ × 29¹

Step-2: Prime Factorization of 23680

Prime factors of 23680 are 2, 5, 37. Prime factorization of 23680 in exponential form is:

23680 = 2⁷ × 5¹ × 37¹

Step-3: Factors of 23664

List of positive integer factors of 23664 that divides 23664 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 29, 34, 48, 51, 58, 68, 87, 102, 116, 136, 174, 204, 232, 272, 348, 408, 464, 493, 696, 816, 986, 1392, 1479, 1972, 2958, 3944, 5916, 7888, 11832

Step-4: Factors of 23680

List of positive integer factors of 23680 that divides 23664 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 37, 40, 64, 74, 80, 128, 148, 160, 185, 296, 320, 370, 592, 640, 740, 1184, 1480, 2368, 2960, 4736, 5920, 11840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23664 and 23680. The biggest common factor number is the GCF number.
So the greatest common factor 23664 and 23680 is 16.

Also check out the Least Common Multiple of 23664 and 23680