What is the Greatest Common Factor of 73200 and 73218?

Greatest common factor (GCF) of 73200 and 73218 is 6.

GCF(73200,73218) = 6

We will now calculate the prime factors of 73200 and 73218, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73200 and 73218.

How to find the GCF of 73200 and 73218?

We will first find the prime factorization of 73200 and 73218. After we will calculate the factors of 73200 and 73218 and find the biggest common factor number .

Step-1: Prime Factorization of 73200

Prime factors of 73200 are 2, 3, 5, 61. Prime factorization of 73200 in exponential form is:

73200 = 2⁴ × 3¹ × 5² × 61¹

Step-2: Prime Factorization of 73218

Prime factors of 73218 are 2, 3, 12203. Prime factorization of 73218 in exponential form is:

73218 = 2¹ × 3¹ × 12203¹

Step-3: Factors of 73200

List of positive integer factors of 73200 that divides 73200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 61, 75, 80, 100, 120, 122, 150, 183, 200, 240, 244, 300, 305, 366, 400, 488, 600, 610, 732, 915, 976, 1200, 1220, 1464, 1525, 1830, 2440, 2928, 3050, 3660, 4575, 4880, 6100, 7320, 9150, 12200, 14640, 18300, 24400, 36600

Step-4: Factors of 73218

List of positive integer factors of 73218 that divides 73200 without a remainder.

1, 2, 3, 6, 12203, 24406, 36609

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73200 and 73218. The biggest common factor number is the GCF number.
So the greatest common factor 73200 and 73218 is 6.

Also check out the Least Common Multiple of 73200 and 73218