What is the Greatest Common Factor of 75306 and 75314?

Greatest common factor (GCF) of 75306 and 75314 is 2.

GCF(75306,75314) = 2

We will now calculate the prime factors of 75306 and 75314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75306 and 75314.

How to find the GCF of 75306 and 75314?

We will first find the prime factorization of 75306 and 75314. After we will calculate the factors of 75306 and 75314 and find the biggest common factor number .

Step-1: Prime Factorization of 75306

Prime factors of 75306 are 2, 3, 7, 11, 163. Prime factorization of 75306 in exponential form is:

75306 = 2¹ × 3¹ × 7¹ × 11¹ × 163¹

Step-2: Prime Factorization of 75314

Prime factors of 75314 are 2, 37657. Prime factorization of 75314 in exponential form is:

75314 = 2¹ × 37657¹

Step-3: Factors of 75306

List of positive integer factors of 75306 that divides 75306 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 163, 231, 326, 462, 489, 978, 1141, 1793, 2282, 3423, 3586, 5379, 6846, 10758, 12551, 25102, 37653

Step-4: Factors of 75314

List of positive integer factors of 75314 that divides 75306 without a remainder.

1, 2, 37657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75306 and 75314. The biggest common factor number is the GCF number.
So the greatest common factor 75306 and 75314 is 2.

Also check out the Least Common Multiple of 75306 and 75314