What is the Greatest Common Factor of 23744 and 23760?

Greatest common factor (GCF) of 23744 and 23760 is 16.

GCF(23744,23760) = 16

We will now calculate the prime factors of 23744 and 23760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23744 and 23760.

How to find the GCF of 23744 and 23760?

We will first find the prime factorization of 23744 and 23760. After we will calculate the factors of 23744 and 23760 and find the biggest common factor number .

Step-1: Prime Factorization of 23744

Prime factors of 23744 are 2, 7, 53. Prime factorization of 23744 in exponential form is:

23744 = 2⁶ × 7¹ × 53¹

Step-2: Prime Factorization of 23760

Prime factors of 23760 are 2, 3, 5, 11. Prime factorization of 23760 in exponential form is:

23760 = 2⁴ × 3³ × 5¹ × 11¹

Step-3: Factors of 23744

List of positive integer factors of 23744 that divides 23744 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 53, 56, 64, 106, 112, 212, 224, 371, 424, 448, 742, 848, 1484, 1696, 2968, 3392, 5936, 11872

Step-4: Factors of 23760

List of positive integer factors of 23760 that divides 23744 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 40, 44, 45, 48, 54, 55, 60, 66, 72, 80, 88, 90, 99, 108, 110, 120, 132, 135, 144, 165, 176, 180, 198, 216, 220, 240, 264, 270, 297, 330, 360, 396, 432, 440, 495, 528, 540, 594, 660, 720, 792, 880, 990, 1080, 1188, 1320, 1485, 1584, 1980, 2160, 2376, 2640, 2970, 3960, 4752, 5940, 7920, 11880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23744 and 23760. The biggest common factor number is the GCF number.
So the greatest common factor 23744 and 23760 is 16.

Also check out the Least Common Multiple of 23744 and 23760