What is the Greatest Common Factor of 3675 and 3688?

Greatest common factor (GCF) of 3675 and 3688 is 1.

GCF(3675,3688) = 1

We will now calculate the prime factors of 3675 and 3688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3675 and 3688.

How to find the GCF of 3675 and 3688?

We will first find the prime factorization of 3675 and 3688. After we will calculate the factors of 3675 and 3688 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 3688

Prime factors of 3688 are 2, 461. Prime factorization of 3688 in exponential form is:

3688 = 2³ × 461¹

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 3688

List of positive integer factors of 3688 that divides 3675 without a remainder.

1, 2, 4, 8, 461, 922, 1844

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3675 and 3688. The biggest common factor number is the GCF number.
So the greatest common factor 3675 and 3688 is 1.

Also check out the Least Common Multiple of 3675 and 3688