What is the Greatest Common Factor of 39675 and 39684?

Greatest common factor (GCF) of 39675 and 39684 is 3.

GCF(39675,39684) = 3

We will now calculate the prime factors of 39675 and 39684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39675 and 39684.

How to find the GCF of 39675 and 39684?

We will first find the prime factorization of 39675 and 39684. After we will calculate the factors of 39675 and 39684 and find the biggest common factor number .

Step-1: Prime Factorization of 39675

Prime factors of 39675 are 3, 5, 23. Prime factorization of 39675 in exponential form is:

39675 = 3¹ × 5² × 23²

Step-2: Prime Factorization of 39684

Prime factors of 39684 are 2, 3, 3307. Prime factorization of 39684 in exponential form is:

39684 = 2² × 3¹ × 3307¹

Step-3: Factors of 39675

List of positive integer factors of 39675 that divides 39675 without a remainder.

1, 3, 5, 15, 23, 25, 69, 75, 115, 345, 529, 575, 1587, 1725, 2645, 7935, 13225

Step-4: Factors of 39684

List of positive integer factors of 39684 that divides 39675 without a remainder.

1, 2, 3, 4, 6, 12, 3307, 6614, 9921, 13228, 19842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39675 and 39684. The biggest common factor number is the GCF number.
So the greatest common factor 39675 and 39684 is 3.

Also check out the Least Common Multiple of 39675 and 39684