What is the Greatest Common Factor of 3675 and 3689?

Greatest common factor (GCF) of 3675 and 3689 is 7.

GCF(3675,3689) = 7

We will now calculate the prime factors of 3675 and 3689, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3675 and 3689.

How to find the GCF of 3675 and 3689?

We will first find the prime factorization of 3675 and 3689. After we will calculate the factors of 3675 and 3689 and find the biggest common factor number .

Step-1: Prime Factorization of 3675

Prime factors of 3675 are 3, 5, 7. Prime factorization of 3675 in exponential form is:

3675 = 3¹ × 5² × 7²

Step-2: Prime Factorization of 3689

Prime factors of 3689 are 7, 17, 31. Prime factorization of 3689 in exponential form is:

3689 = 7¹ × 17¹ × 31¹

Step-3: Factors of 3675

List of positive integer factors of 3675 that divides 3675 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225

Step-4: Factors of 3689

List of positive integer factors of 3689 that divides 3675 without a remainder.

1, 7, 17, 31, 119, 217, 527

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3675 and 3689. The biggest common factor number is the GCF number.
So the greatest common factor 3675 and 3689 is 7.

Also check out the Least Common Multiple of 3675 and 3689