What is the Greatest Common Factor of 75299 and 75306?

Greatest common factor (GCF) of 75299 and 75306 is 7.

GCF(75299,75306) = 7

We will now calculate the prime factors of 75299 and 75306, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75299 and 75306.

How to find the GCF of 75299 and 75306?

We will first find the prime factorization of 75299 and 75306. After we will calculate the factors of 75299 and 75306 and find the biggest common factor number .

Step-1: Prime Factorization of 75299

Prime factors of 75299 are 7, 31, 347. Prime factorization of 75299 in exponential form is:

75299 = 7¹ × 31¹ × 347¹

Step-2: 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-3: Factors of 75299

List of positive integer factors of 75299 that divides 75299 without a remainder.

1, 7, 31, 217, 347, 2429, 10757

Step-4: Factors of 75306

List of positive integer factors of 75306 that divides 75299 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75299 and 75306. The biggest common factor number is the GCF number.
So the greatest common factor 75299 and 75306 is 7.

Also check out the Least Common Multiple of 75299 and 75306