What is the Greatest Common Factor of 85300 and 85314?

Greatest common factor (GCF) of 85300 and 85314 is 2.

GCF(85300,85314) = 2

We will now calculate the prime factors of 85300 and 85314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85300 and 85314.

How to find the GCF of 85300 and 85314?

We will first find the prime factorization of 85300 and 85314. After we will calculate the factors of 85300 and 85314 and find the biggest common factor number .

Step-1: Prime Factorization of 85300

Prime factors of 85300 are 2, 5, 853. Prime factorization of 85300 in exponential form is:

85300 = 2² × 5² × 853¹

Step-2: Prime Factorization of 85314

Prime factors of 85314 are 2, 3, 59, 241. Prime factorization of 85314 in exponential form is:

85314 = 2¹ × 3¹ × 59¹ × 241¹

Step-3: Factors of 85300

List of positive integer factors of 85300 that divides 85300 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 853, 1706, 3412, 4265, 8530, 17060, 21325, 42650

Step-4: Factors of 85314

List of positive integer factors of 85314 that divides 85300 without a remainder.

1, 2, 3, 6, 59, 118, 177, 241, 354, 482, 723, 1446, 14219, 28438, 42657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85300 and 85314. The biggest common factor number is the GCF number.
So the greatest common factor 85300 and 85314 is 2.

Also check out the Least Common Multiple of 85300 and 85314