What is the Greatest Common Factor of 23970 and 23985?

Greatest common factor (GCF) of 23970 and 23985 is 15.

GCF(23970,23985) = 15

We will now calculate the prime factors of 23970 and 23985, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23970 and 23985.

How to find the GCF of 23970 and 23985?

We will first find the prime factorization of 23970 and 23985. After we will calculate the factors of 23970 and 23985 and find the biggest common factor number .

Step-1: Prime Factorization of 23970

Prime factors of 23970 are 2, 3, 5, 17, 47. Prime factorization of 23970 in exponential form is:

23970 = 2¹ × 3¹ × 5¹ × 17¹ × 47¹

Step-2: Prime Factorization of 23985

Prime factors of 23985 are 3, 5, 13, 41. Prime factorization of 23985 in exponential form is:

23985 = 3² × 5¹ × 13¹ × 41¹

Step-3: Factors of 23970

List of positive integer factors of 23970 that divides 23970 without a remainder.

1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 47, 51, 85, 94, 102, 141, 170, 235, 255, 282, 470, 510, 705, 799, 1410, 1598, 2397, 3995, 4794, 7990, 11985

Step-4: Factors of 23985

List of positive integer factors of 23985 that divides 23970 without a remainder.

1, 3, 5, 9, 13, 15, 39, 41, 45, 65, 117, 123, 195, 205, 369, 533, 585, 615, 1599, 1845, 2665, 4797, 7995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23970 and 23985. The biggest common factor number is the GCF number.
So the greatest common factor 23970 and 23985 is 15.

Also check out the Least Common Multiple of 23970 and 23985