What is the Greatest Common Factor of 75309 and 75320?

Greatest common factor (GCF) of 75309 and 75320 is 1.

GCF(75309,75320) = 1

We will now calculate the prime factors of 75309 and 75320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75309 and 75320.

How to find the GCF of 75309 and 75320?

We will first find the prime factorization of 75309 and 75320. After we will calculate the factors of 75309 and 75320 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 75320

Prime factors of 75320 are 2, 5, 7, 269. Prime factorization of 75320 in exponential form is:

75320 = 2³ × 5¹ × 7¹ × 269¹

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 75320

List of positive integer factors of 75320 that divides 75309 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 269, 280, 538, 1076, 1345, 1883, 2152, 2690, 3766, 5380, 7532, 9415, 10760, 15064, 18830, 37660

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75309 and 75320. The biggest common factor number is the GCF number.
So the greatest common factor 75309 and 75320 is 1.

Also check out the Least Common Multiple of 75309 and 75320