What is the Greatest Common Factor of 3509 and 3514?

Greatest common factor (GCF) of 3509 and 3514 is 1.

GCF(3509,3514) = 1

We will now calculate the prime factors of 3509 and 3514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3509 and 3514.

How to find the GCF of 3509 and 3514?

We will first find the prime factorization of 3509 and 3514. After we will calculate the factors of 3509 and 3514 and find the biggest common factor number .

Step-1: Prime Factorization of 3509

Prime factors of 3509 are 11, 29. Prime factorization of 3509 in exponential form is:

3509 = 11² × 29¹

Step-2: Prime Factorization of 3514

Prime factors of 3514 are 2, 7, 251. Prime factorization of 3514 in exponential form is:

3514 = 2¹ × 7¹ × 251¹

Step-3: Factors of 3509

List of positive integer factors of 3509 that divides 3509 without a remainder.

1, 11, 29, 121, 319

Step-4: Factors of 3514

List of positive integer factors of 3514 that divides 3509 without a remainder.

1, 2, 7, 14, 251, 502, 1757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3509 and 3514. The biggest common factor number is the GCF number.
So the greatest common factor 3509 and 3514 is 1.

Also check out the Least Common Multiple of 3509 and 3514