What is the Greatest Common Factor of 74300 and 74314?

Greatest common factor (GCF) of 74300 and 74314 is 2.

GCF(74300,74314) = 2

We will now calculate the prime factors of 74300 and 74314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74300 and 74314.

How to find the GCF of 74300 and 74314?

We will first find the prime factorization of 74300 and 74314. After we will calculate the factors of 74300 and 74314 and find the biggest common factor number .

Step-1: Prime Factorization of 74300

Prime factors of 74300 are 2, 5, 743. Prime factorization of 74300 in exponential form is:

74300 = 2² × 5² × 743¹

Step-2: Prime Factorization of 74314

Prime factors of 74314 are 2, 73, 509. Prime factorization of 74314 in exponential form is:

74314 = 2¹ × 73¹ × 509¹

Step-3: Factors of 74300

List of positive integer factors of 74300 that divides 74300 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 743, 1486, 2972, 3715, 7430, 14860, 18575, 37150

Step-4: Factors of 74314

List of positive integer factors of 74314 that divides 74300 without a remainder.

1, 2, 73, 146, 509, 1018, 37157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74300 and 74314. The biggest common factor number is the GCF number.
So the greatest common factor 74300 and 74314 is 2.

Also check out the Least Common Multiple of 74300 and 74314