What is the Greatest Common Factor of 39690 and 39704?

Greatest common factor (GCF) of 39690 and 39704 is 14.

GCF(39690,39704) = 14

We will now calculate the prime factors of 39690 and 39704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39690 and 39704.

How to find the GCF of 39690 and 39704?

We will first find the prime factorization of 39690 and 39704. After we will calculate the factors of 39690 and 39704 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39704

Prime factors of 39704 are 2, 7, 709. Prime factorization of 39704 in exponential form is:

39704 = 2³ × 7¹ × 709¹

Step-3: Factors of 39690

List of positive integer factors of 39690 that divides 39690 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

Step-4: Factors of 39704

List of positive integer factors of 39704 that divides 39690 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 709, 1418, 2836, 4963, 5672, 9926, 19852

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39690 and 39704. The biggest common factor number is the GCF number.
So the greatest common factor 39690 and 39704 is 14.

Also check out the Least Common Multiple of 39690 and 39704