What is the Greatest Common Factor of 23760 and 23780?

Greatest common factor (GCF) of 23760 and 23780 is 20.

GCF(23760,23780) = 20

We will now calculate the prime factors of 23760 and 23780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23760 and 23780.

How to find the GCF of 23760 and 23780?

We will first find the prime factorization of 23760 and 23780. After we will calculate the factors of 23760 and 23780 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 23780

Prime factors of 23780 are 2, 5, 29, 41. Prime factorization of 23780 in exponential form is:

23780 = 2² × 5¹ × 29¹ × 41¹

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 23780

List of positive integer factors of 23780 that divides 23760 without a remainder.

1, 2, 4, 5, 10, 20, 29, 41, 58, 82, 116, 145, 164, 205, 290, 410, 580, 820, 1189, 2378, 4756, 5945, 11890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23760 and 23780. The biggest common factor number is the GCF number.
So the greatest common factor 23760 and 23780 is 20.

Also check out the Least Common Multiple of 23760 and 23780