What is the Greatest Common Factor of 72300 and 72314?

Greatest common factor (GCF) of 72300 and 72314 is 2.

GCF(72300,72314) = 2

We will now calculate the prime factors of 72300 and 72314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72300 and 72314.

How to find the GCF of 72300 and 72314?

We will first find the prime factorization of 72300 and 72314. After we will calculate the factors of 72300 and 72314 and find the biggest common factor number .

Step-1: Prime Factorization of 72300

Prime factors of 72300 are 2, 3, 5, 241. Prime factorization of 72300 in exponential form is:

72300 = 2² × 3¹ × 5² × 241¹

Step-2: Prime Factorization of 72314

Prime factors of 72314 are 2, 11, 19, 173. Prime factorization of 72314 in exponential form is:

72314 = 2¹ × 11¹ × 19¹ × 173¹

Step-3: Factors of 72300

List of positive integer factors of 72300 that divides 72300 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 241, 300, 482, 723, 964, 1205, 1446, 2410, 2892, 3615, 4820, 6025, 7230, 12050, 14460, 18075, 24100, 36150

Step-4: Factors of 72314

List of positive integer factors of 72314 that divides 72300 without a remainder.

1, 2, 11, 19, 22, 38, 173, 209, 346, 418, 1903, 3287, 3806, 6574, 36157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72300 and 72314. The biggest common factor number is the GCF number.
So the greatest common factor 72300 and 72314 is 2.

Also check out the Least Common Multiple of 72300 and 72314