What is the Greatest Common Factor of 19712 and 19723?

Greatest common factor (GCF) of 19712 and 19723 is 11.

GCF(19712,19723) = 11

We will now calculate the prime factors of 19712 and 19723, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19712 and 19723.

How to find the GCF of 19712 and 19723?

We will first find the prime factorization of 19712 and 19723. After we will calculate the factors of 19712 and 19723 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19723

Prime factors of 19723 are 11, 163. Prime factorization of 19723 in exponential form is:

19723 = 11² × 163¹

Step-3: Factors of 19712

List of positive integer factors of 19712 that divides 19712 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

Step-4: Factors of 19723

List of positive integer factors of 19723 that divides 19712 without a remainder.

1, 11, 121, 163, 1793

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19712 and 19723. The biggest common factor number is the GCF number.
So the greatest common factor 19712 and 19723 is 11.

Also check out the Least Common Multiple of 19712 and 19723