What is the Greatest Common Factor of 23520 and 23538?

Greatest common factor (GCF) of 23520 and 23538 is 6.

GCF(23520,23538) = 6

We will now calculate the prime factors of 23520 and 23538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23520 and 23538.

How to find the GCF of 23520 and 23538?

We will first find the prime factorization of 23520 and 23538. After we will calculate the factors of 23520 and 23538 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 23538

Prime factors of 23538 are 2, 3, 3923. Prime factorization of 23538 in exponential form is:

23538 = 2¹ × 3¹ × 3923¹

Step-3: Factors of 23520

List of positive integer factors of 23520 that divides 23520 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

Step-4: Factors of 23538

List of positive integer factors of 23538 that divides 23520 without a remainder.

1, 2, 3, 6, 3923, 7846, 11769

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23520 and 23538. The biggest common factor number is the GCF number.
So the greatest common factor 23520 and 23538 is 6.

Also check out the Least Common Multiple of 23520 and 23538