What is the Greatest Common Factor of 19704 and 19722?

Greatest common factor (GCF) of 19704 and 19722 is 6.

GCF(19704,19722) = 6

We will now calculate the prime factors of 19704 and 19722, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19704 and 19722.

How to find the GCF of 19704 and 19722?

We will first find the prime factorization of 19704 and 19722. After we will calculate the factors of 19704 and 19722 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 19722

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

19722 = 2¹ × 3¹ × 19¹ × 173¹

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 19722

List of positive integer factors of 19722 that divides 19704 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19704 and 19722. The biggest common factor number is the GCF number.
So the greatest common factor 19704 and 19722 is 6.

Also check out the Least Common Multiple of 19704 and 19722