What is the Greatest Common Factor of 23500 and 23520?

Greatest common factor (GCF) of 23500 and 23520 is 20.

GCF(23500,23520) = 20

We will now calculate the prime factors of 23500 and 23520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23500 and 23520.

How to find the GCF of 23500 and 23520?

We will first find the prime factorization of 23500 and 23520. After we will calculate the factors of 23500 and 23520 and find the biggest common factor number .

Step-1: Prime Factorization of 23500

Prime factors of 23500 are 2, 5, 47. Prime factorization of 23500 in exponential form is:

23500 = 2² × 5³ × 47¹

Step-2: Prime Factorization of 23520

Prime factors of 23520 are 2, 3, 5, 7. Prime factorization of 23520 in exponential form is:

23520 = 2⁵ × 3¹ × 5¹ × 7²

Step-3: Factors of 23500

List of positive integer factors of 23500 that divides 23500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 47, 50, 94, 100, 125, 188, 235, 250, 470, 500, 940, 1175, 2350, 4700, 5875, 11750

Step-4: Factors of 23520

List of positive integer factors of 23520 that divides 23500 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 49, 56, 60, 70, 80, 84, 96, 98, 105, 112, 120, 140, 147, 160, 168, 196, 210, 224, 240, 245, 280, 294, 336, 392, 420, 480, 490, 560, 588, 672, 735, 784, 840, 980, 1120, 1176, 1470, 1568, 1680, 1960, 2352, 2940, 3360, 3920, 4704, 5880, 7840, 11760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23500 and 23520. The biggest common factor number is the GCF number.
So the greatest common factor 23500 and 23520 is 20.

Also check out the Least Common Multiple of 23500 and 23520