What is the Greatest Common Factor of 39696 and 39704?

Greatest common factor (GCF) of 39696 and 39704 is 8.

GCF(39696,39704) = 8

We will now calculate the prime factors of 39696 and 39704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39696 and 39704.

How to find the GCF of 39696 and 39704?

We will first find the prime factorization of 39696 and 39704. After we will calculate the factors of 39696 and 39704 and find the biggest common factor number .

Step-1: Prime Factorization of 39696

Prime factors of 39696 are 2, 3, 827. Prime factorization of 39696 in exponential form is:

39696 = 2⁴ × 3¹ × 827¹

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 39696

List of positive integer factors of 39696 that divides 39696 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 827, 1654, 2481, 3308, 4962, 6616, 9924, 13232, 19848

Step-4: Factors of 39704

List of positive integer factors of 39704 that divides 39696 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 39696 and 39704. The biggest common factor number is the GCF number.
So the greatest common factor 39696 and 39704 is 8.

Also check out the Least Common Multiple of 39696 and 39704