What is the Greatest Common Factor of 39675 and 39690?

Greatest common factor (GCF) of 39675 and 39690 is 15.

GCF(39675,39690) = 15

We will now calculate the prime factors of 39675 and 39690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39675 and 39690.

How to find the GCF of 39675 and 39690?

We will first find the prime factorization of 39675 and 39690. After we will calculate the factors of 39675 and 39690 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 39690

Prime factors of 39690 are 2, 3, 5, 7. Prime factorization of 39690 in exponential form is:

39690 = 2¹ × 3⁴ × 5¹ × 7²

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 39690

List of positive integer factors of 39690 that divides 39675 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 49, 54, 63, 70, 81, 90, 98, 105, 126, 135, 147, 162, 189, 210, 245, 270, 294, 315, 378, 405, 441, 490, 567, 630, 735, 810, 882, 945, 1134, 1323, 1470, 1890, 2205, 2646, 2835, 3969, 4410, 5670, 6615, 7938, 13230, 19845

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39675 and 39690. The biggest common factor number is the GCF number.
So the greatest common factor 39675 and 39690 is 15.

Also check out the Least Common Multiple of 39675 and 39690