What is the Greatest Common Factor of 19728 and 19746?

Greatest common factor (GCF) of 19728 and 19746 is 18.

GCF(19728,19746) = 18

We will now calculate the prime factors of 19728 and 19746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19728 and 19746.

How to find the GCF of 19728 and 19746?

We will first find the prime factorization of 19728 and 19746. After we will calculate the factors of 19728 and 19746 and find the biggest common factor number .

Step-1: Prime Factorization of 19728

Prime factors of 19728 are 2, 3, 137. Prime factorization of 19728 in exponential form is:

19728 = 2⁴ × 3² × 137¹

Step-2: Prime Factorization of 19746

Prime factors of 19746 are 2, 3, 1097. Prime factorization of 19746 in exponential form is:

19746 = 2¹ × 3² × 1097¹

Step-3: Factors of 19728

List of positive integer factors of 19728 that divides 19728 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 137, 144, 274, 411, 548, 822, 1096, 1233, 1644, 2192, 2466, 3288, 4932, 6576, 9864

Step-4: Factors of 19746

List of positive integer factors of 19746 that divides 19728 without a remainder.

1, 2, 3, 6, 9, 18, 1097, 2194, 3291, 6582, 9873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19728 and 19746. The biggest common factor number is the GCF number.
So the greatest common factor 19728 and 19746 is 18.

Also check out the Least Common Multiple of 19728 and 19746