What is the Greatest Common Factor of 19704 and 19712?

Greatest common factor (GCF) of 19704 and 19712 is 8.

GCF(19704,19712) = 8

We will now calculate the prime factors of 19704 and 19712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19704 and 19712.

How to find the GCF of 19704 and 19712?

We will first find the prime factorization of 19704 and 19712. After we will calculate the factors of 19704 and 19712 and find the biggest common factor number .

Step-1: Prime Factorization of 19704

Prime factors of 19704 are 2, 3, 821. Prime factorization of 19704 in exponential form is:

19704 = 2³ × 3¹ × 821¹

Step-2: Prime Factorization of 19712

Prime factors of 19712 are 2, 7, 11. Prime factorization of 19712 in exponential form is:

19712 = 2⁸ × 7¹ × 11¹

Step-3: Factors of 19704

List of positive integer factors of 19704 that divides 19704 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 821, 1642, 2463, 3284, 4926, 6568, 9852

Step-4: Factors of 19712

List of positive integer factors of 19712 that divides 19704 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 32, 44, 56, 64, 77, 88, 112, 128, 154, 176, 224, 256, 308, 352, 448, 616, 704, 896, 1232, 1408, 1792, 2464, 2816, 4928, 9856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19704 and 19712. The biggest common factor number is the GCF number.
So the greatest common factor 19704 and 19712 is 8.

Also check out the Least Common Multiple of 19704 and 19712