What is the Greatest Common Factor of 19722 and 19728?

Greatest common factor (GCF) of 19722 and 19728 is 6.

GCF(19722,19728) = 6

We will now calculate the prime factors of 19722 and 19728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19722 and 19728.

How to find the GCF of 19722 and 19728?

We will first find the prime factorization of 19722 and 19728. After we will calculate the factors of 19722 and 19728 and find the biggest common factor number .

Step-1: Prime Factorization of 19722

Prime factors of 19722 are 2, 3, 19, 173. Prime factorization of 19722 in exponential form is:

19722 = 2¹ × 3¹ × 19¹ × 173¹

Step-2: 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-3: Factors of 19722

List of positive integer factors of 19722 that divides 19722 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114, 173, 346, 519, 1038, 3287, 6574, 9861

Step-4: Factors of 19728

List of positive integer factors of 19728 that divides 19722 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19722 and 19728. The biggest common factor number is the GCF number.
So the greatest common factor 19722 and 19728 is 6.

Also check out the Least Common Multiple of 19722 and 19728