What is the Greatest Common Factor of 72400 and 72414?

Greatest common factor (GCF) of 72400 and 72414 is 2.

GCF(72400,72414) = 2

We will now calculate the prime factors of 72400 and 72414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72400 and 72414.

How to find the GCF of 72400 and 72414?

We will first find the prime factorization of 72400 and 72414. After we will calculate the factors of 72400 and 72414 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 72414

Prime factors of 72414 are 2, 3, 149. Prime factorization of 72414 in exponential form is:

72414 = 2¹ × 3⁵ × 149¹

Step-3: Factors of 72400

List of positive integer factors of 72400 that divides 72400 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

Step-4: Factors of 72414

List of positive integer factors of 72414 that divides 72400 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 149, 162, 243, 298, 447, 486, 894, 1341, 2682, 4023, 8046, 12069, 24138, 36207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72400 and 72414. The biggest common factor number is the GCF number.
So the greatest common factor 72400 and 72414 is 2.

Also check out the Least Common Multiple of 72400 and 72414