What is the Greatest Common Factor of 72384 and 72400?

Greatest common factor (GCF) of 72384 and 72400 is 16.

GCF(72384,72400) = 16

We will now calculate the prime factors of 72384 and 72400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72384 and 72400.

How to find the GCF of 72384 and 72400?

We will first find the prime factorization of 72384 and 72400. After we will calculate the factors of 72384 and 72400 and find the biggest common factor number .

Step-1: Prime Factorization of 72384

Prime factors of 72384 are 2, 3, 13, 29. Prime factorization of 72384 in exponential form is:

72384 = 2⁶ × 3¹ × 13¹ × 29¹

Step-2: Prime Factorization of 72400

Prime factors of 72400 are 2, 5, 181. Prime factorization of 72400 in exponential form is:

72400 = 2⁴ × 5² × 181¹

Step-3: Factors of 72384

List of positive integer factors of 72384 that divides 72384 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 29, 32, 39, 48, 52, 58, 64, 78, 87, 96, 104, 116, 156, 174, 192, 208, 232, 312, 348, 377, 416, 464, 624, 696, 754, 832, 928, 1131, 1248, 1392, 1508, 1856, 2262, 2496, 2784, 3016, 4524, 5568, 6032, 9048, 12064, 18096, 24128, 36192

Step-4: Factors of 72400

List of positive integer factors of 72400 that divides 72384 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 181, 200, 362, 400, 724, 905, 1448, 1810, 2896, 3620, 4525, 7240, 9050, 14480, 18100, 36200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72384 and 72400. The biggest common factor number is the GCF number.
So the greatest common factor 72384 and 72400 is 16.

Also check out the Least Common Multiple of 72384 and 72400