What is the Greatest Common Factor of 39684 and 39696?

Greatest common factor (GCF) of 39684 and 39696 is 12.

GCF(39684,39696) = 12

We will now calculate the prime factors of 39684 and 39696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39684 and 39696.

How to find the GCF of 39684 and 39696?

We will first find the prime factorization of 39684 and 39696. After we will calculate the factors of 39684 and 39696 and find the biggest common factor number .

Step-1: 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-2: 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-3: Factors of 39684

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

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

Step-4: Factors of 39696

List of positive integer factors of 39696 that divides 39684 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39684 and 39696. The biggest common factor number is the GCF number.
So the greatest common factor 39684 and 39696 is 12.

Also check out the Least Common Multiple of 39684 and 39696