What is the Greatest Common Factor of 23505 and 23520?

Greatest common factor (GCF) of 23505 and 23520 is 15.

GCF(23505,23520) = 15

We will now calculate the prime factors of 23505 and 23520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23505 and 23520.

How to find the GCF of 23505 and 23520?

We will first find the prime factorization of 23505 and 23520. After we will calculate the factors of 23505 and 23520 and find the biggest common factor number .

Step-1: Prime Factorization of 23505

Prime factors of 23505 are 3, 5, 1567. Prime factorization of 23505 in exponential form is:

23505 = 3¹ × 5¹ × 1567¹

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 23505

List of positive integer factors of 23505 that divides 23505 without a remainder.

1, 3, 5, 15, 1567, 4701, 7835

Step-4: Factors of 23520

List of positive integer factors of 23520 that divides 23505 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 23505 and 23520. The biggest common factor number is the GCF number.
So the greatest common factor 23505 and 23520 is 15.

Also check out the Least Common Multiple of 23505 and 23520