What is the Greatest Common Factor of 19698 and 19712?

Greatest common factor (GCF) of 19698 and 19712 is 14.

GCF(19698,19712) = 14

We will now calculate the prime factors of 19698 and 19712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19698 and 19712.

How to find the GCF of 19698 and 19712?

We will first find the prime factorization of 19698 and 19712. After we will calculate the factors of 19698 and 19712 and find the biggest common factor number .

Step-1: Prime Factorization of 19698

Prime factors of 19698 are 2, 3, 7, 67. Prime factorization of 19698 in exponential form is:

19698 = 2¹ × 3¹ × 7² × 67¹

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 19698

List of positive integer factors of 19698 that divides 19698 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 49, 67, 98, 134, 147, 201, 294, 402, 469, 938, 1407, 2814, 3283, 6566, 9849

Step-4: Factors of 19712

List of positive integer factors of 19712 that divides 19698 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 19698 and 19712. The biggest common factor number is the GCF number.
So the greatest common factor 19698 and 19712 is 14.

Also check out the Least Common Multiple of 19698 and 19712