What is the Greatest Common Factor of 3500 and 3509?

Greatest common factor (GCF) of 3500 and 3509 is 1.

GCF(3500,3509) = 1

We will now calculate the prime factors of 3500 and 3509, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3500 and 3509.

How to find the GCF of 3500 and 3509?

We will first find the prime factorization of 3500 and 3509. After we will calculate the factors of 3500 and 3509 and find the biggest common factor number .

Step-1: Prime Factorization of 3500

Prime factors of 3500 are 2, 5, 7. Prime factorization of 3500 in exponential form is:

3500 = 2² × 5³ × 7¹

Step-2: Prime Factorization of 3509

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

3509 = 11² × 29¹

Step-3: Factors of 3500

List of positive integer factors of 3500 that divides 3500 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750

Step-4: Factors of 3509

List of positive integer factors of 3509 that divides 3500 without a remainder.

1, 11, 29, 121, 319

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3500 and 3509. The biggest common factor number is the GCF number.
So the greatest common factor 3500 and 3509 is 1.

Also check out the Least Common Multiple of 3500 and 3509