What is the Greatest Common Factor of 23760 and 23772?

Greatest common factor (GCF) of 23760 and 23772 is 12.

GCF(23760,23772) = 12

We will now calculate the prime factors of 23760 and 23772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23760 and 23772.

How to find the GCF of 23760 and 23772?

We will first find the prime factorization of 23760 and 23772. After we will calculate the factors of 23760 and 23772 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 23772

Prime factors of 23772 are 2, 3, 7, 283. Prime factorization of 23772 in exponential form is:

23772 = 2² × 3¹ × 7¹ × 283¹

Step-3: Factors of 23760

List of positive integer factors of 23760 that divides 23760 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

Step-4: Factors of 23772

List of positive integer factors of 23772 that divides 23760 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 283, 566, 849, 1132, 1698, 1981, 3396, 3962, 5943, 7924, 11886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23760 and 23772. The biggest common factor number is the GCF number.
So the greatest common factor 23760 and 23772 is 12.

Also check out the Least Common Multiple of 23760 and 23772