What is the Greatest Common Factor of 73500 and 73510?

Greatest common factor (GCF) of 73500 and 73510 is 10.

GCF(73500,73510) = 10

We will now calculate the prime factors of 73500 and 73510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73500 and 73510.

How to find the GCF of 73500 and 73510?

We will first find the prime factorization of 73500 and 73510. After we will calculate the factors of 73500 and 73510 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 73510

Prime factors of 73510 are 2, 5, 7351. Prime factorization of 73510 in exponential form is:

73510 = 2¹ × 5¹ × 7351¹

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 73510

List of positive integer factors of 73510 that divides 73500 without a remainder.

1, 2, 5, 10, 7351, 14702, 36755

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73500 and 73510. The biggest common factor number is the GCF number.
So the greatest common factor 73500 and 73510 is 10.

Also check out the Least Common Multiple of 73500 and 73510