What is the Greatest Common Factor of 75309 and 75322?

Greatest common factor (GCF) of 75309 and 75322 is 13.

GCF(75309,75322) = 13

We will now calculate the prime factors of 75309 and 75322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75309 and 75322.

How to find the GCF of 75309 and 75322?

We will first find the prime factorization of 75309 and 75322. After we will calculate the factors of 75309 and 75322 and find the biggest common factor number .

Step-1: Prime Factorization of 75309

Prime factors of 75309 are 3, 13, 1931. Prime factorization of 75309 in exponential form is:

75309 = 3¹ × 13¹ × 1931¹

Step-2: Prime Factorization of 75322

Prime factors of 75322 are 2, 13, 2897. Prime factorization of 75322 in exponential form is:

75322 = 2¹ × 13¹ × 2897¹

Step-3: Factors of 75309

List of positive integer factors of 75309 that divides 75309 without a remainder.

1, 3, 13, 39, 1931, 5793, 25103

Step-4: Factors of 75322

List of positive integer factors of 75322 that divides 75309 without a remainder.

1, 2, 13, 26, 2897, 5794, 37661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75309 and 75322. The biggest common factor number is the GCF number.
So the greatest common factor 75309 and 75322 is 13.

Also check out the Least Common Multiple of 75309 and 75322