What is the Greatest Common Factor of 23685 and 23700?

Greatest common factor (GCF) of 23685 and 23700 is 15.

GCF(23685,23700) = 15

We will now calculate the prime factors of 23685 and 23700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23685 and 23700.

How to find the GCF of 23685 and 23700?

We will first find the prime factorization of 23685 and 23700. After we will calculate the factors of 23685 and 23700 and find the biggest common factor number .

Step-1: Prime Factorization of 23685

Prime factors of 23685 are 3, 5, 1579. Prime factorization of 23685 in exponential form is:

23685 = 3¹ × 5¹ × 1579¹

Step-2: Prime Factorization of 23700

Prime factors of 23700 are 2, 3, 5, 79. Prime factorization of 23700 in exponential form is:

23700 = 2² × 3¹ × 5² × 79¹

Step-3: Factors of 23685

List of positive integer factors of 23685 that divides 23685 without a remainder.

1, 3, 5, 15, 1579, 4737, 7895

Step-4: Factors of 23700

List of positive integer factors of 23700 that divides 23685 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 79, 100, 150, 158, 237, 300, 316, 395, 474, 790, 948, 1185, 1580, 1975, 2370, 3950, 4740, 5925, 7900, 11850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23685 and 23700. The biggest common factor number is the GCF number.
So the greatest common factor 23685 and 23700 is 15.

Also check out the Least Common Multiple of 23685 and 23700