What is the Greatest Common Factor of 73500 and 73509?

Greatest common factor (GCF) of 73500 and 73509 is 3.

GCF(73500,73509) = 3

We will now calculate the prime factors of 73500 and 73509, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73500 and 73509.

How to find the GCF of 73500 and 73509?

We will first find the prime factorization of 73500 and 73509. After we will calculate the factors of 73500 and 73509 and find the biggest common factor number .

Step-1: Prime Factorization of 73500

Prime factors of 73500 are 2, 3, 5, 7. Prime factorization of 73500 in exponential form is:

73500 = 2² × 3¹ × 5³ × 7²

Step-2: Prime Factorization of 73509

Prime factors of 73509 are 3, 107, 229. Prime factorization of 73509 in exponential form is:

73509 = 3¹ × 107¹ × 229¹

Step-3: Factors of 73500

List of positive integer factors of 73500 that divides 73500 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 49, 50, 60, 70, 75, 84, 98, 100, 105, 125, 140, 147, 150, 175, 196, 210, 245, 250, 294, 300, 350, 375, 420, 490, 500, 525, 588, 700, 735, 750, 875, 980, 1050, 1225, 1470, 1500, 1750, 2100, 2450, 2625, 2940, 3500, 3675, 4900, 5250, 6125, 7350, 10500, 12250, 14700, 18375, 24500, 36750

Step-4: Factors of 73509

List of positive integer factors of 73509 that divides 73500 without a remainder.

1, 3, 107, 229, 321, 687, 24503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73500 and 73509. The biggest common factor number is the GCF number.
So the greatest common factor 73500 and 73509 is 3.

Also check out the Least Common Multiple of 73500 and 73509