What is the Greatest Common Factor of 73200 and 73219?

Greatest common factor (GCF) of 73200 and 73219 is 1.

GCF(73200,73219) = 1

We will now calculate the prime factors of 73200 and 73219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73200 and 73219.

How to find the GCF of 73200 and 73219?

We will first find the prime factorization of 73200 and 73219. After we will calculate the factors of 73200 and 73219 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 73219

Prime factors of 73219 are 17, 59, 73. Prime factorization of 73219 in exponential form is:

73219 = 17¹ × 59¹ × 73¹

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 73219

List of positive integer factors of 73219 that divides 73200 without a remainder.

1, 17, 59, 73, 1003, 1241, 4307

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73200 and 73219. The biggest common factor number is the GCF number.
So the greatest common factor 73200 and 73219 is 1.

Also check out the Least Common Multiple of 73200 and 73219