What is the Greatest Common Factor of 1509 and 1514?

Greatest common factor (GCF) of 1509 and 1514 is 1.

GCF(1509,1514) = 1

We will now calculate the prime factors of 1509 and 1514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1509 and 1514.

How to find the GCF of 1509 and 1514?

We will first find the prime factorization of 1509 and 1514. After we will calculate the factors of 1509 and 1514 and find the biggest common factor number .

Step-1: Prime Factorization of 1509

Prime factors of 1509 are 3, 503. Prime factorization of 1509 in exponential form is:

1509 = 3¹ × 503¹

Step-2: Prime Factorization of 1514

Prime factors of 1514 are 2, 757. Prime factorization of 1514 in exponential form is:

1514 = 2¹ × 757¹

Step-3: Factors of 1509

List of positive integer factors of 1509 that divides 1509 without a remainder.

1, 3, 503

Step-4: Factors of 1514

List of positive integer factors of 1514 that divides 1509 without a remainder.

1, 2, 757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1509 and 1514. The biggest common factor number is the GCF number.
So the greatest common factor 1509 and 1514 is 1.

Also check out the Least Common Multiple of 1509 and 1514