What is the Greatest Common Factor of 23504 and 23520?

Greatest common factor (GCF) of 23504 and 23520 is 16.

GCF(23504,23520) = 16

We will now calculate the prime factors of 23504 and 23520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23504 and 23520.

How to find the GCF of 23504 and 23520?

We will first find the prime factorization of 23504 and 23520. After we will calculate the factors of 23504 and 23520 and find the biggest common factor number .

Step-1: Prime Factorization of 23504

Prime factors of 23504 are 2, 13, 113. Prime factorization of 23504 in exponential form is:

23504 = 2⁴ × 13¹ × 113¹

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 23504

List of positive integer factors of 23504 that divides 23504 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 113, 208, 226, 452, 904, 1469, 1808, 2938, 5876, 11752

Step-4: Factors of 23520

List of positive integer factors of 23520 that divides 23504 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 23504 and 23520. The biggest common factor number is the GCF number.
So the greatest common factor 23504 and 23520 is 16.

Also check out the Least Common Multiple of 23504 and 23520