What is the Greatest Common Factor of 75509 and 75514?

Greatest common factor (GCF) of 75509 and 75514 is 1.

GCF(75509,75514) = 1

We will now calculate the prime factors of 75509 and 75514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75509 and 75514.

How to find the GCF of 75509 and 75514?

We will first find the prime factorization of 75509 and 75514. After we will calculate the factors of 75509 and 75514 and find the biggest common factor number .

Step-1: Prime Factorization of 75509

Prime factors of 75509 are 7, 23, 67. Prime factorization of 75509 in exponential form is:

75509 = 7² × 23¹ × 67¹

Step-2: Prime Factorization of 75514

Prime factors of 75514 are 2, 17, 2221. Prime factorization of 75514 in exponential form is:

75514 = 2¹ × 17¹ × 2221¹

Step-3: Factors of 75509

List of positive integer factors of 75509 that divides 75509 without a remainder.

1, 7, 23, 49, 67, 161, 469, 1127, 1541, 3283, 10787

Step-4: Factors of 75514

List of positive integer factors of 75514 that divides 75509 without a remainder.

1, 2, 17, 34, 2221, 4442, 37757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75509 and 75514. The biggest common factor number is the GCF number.
So the greatest common factor 75509 and 75514 is 1.

Also check out the Least Common Multiple of 75509 and 75514