What is the Greatest Common Factor of 19688 and 19704?

Greatest common factor (GCF) of 19688 and 19704 is 8.

GCF(19688,19704) = 8

We will now calculate the prime factors of 19688 and 19704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19688 and 19704.

How to find the GCF of 19688 and 19704?

We will first find the prime factorization of 19688 and 19704. After we will calculate the factors of 19688 and 19704 and find the biggest common factor number .

Step-1: Prime Factorization of 19688

Prime factors of 19688 are 2, 23, 107. Prime factorization of 19688 in exponential form is:

19688 = 2³ × 23¹ × 107¹

Step-2: 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-3: Factors of 19688

List of positive integer factors of 19688 that divides 19688 without a remainder.

1, 2, 4, 8, 23, 46, 92, 107, 184, 214, 428, 856, 2461, 4922, 9844

Step-4: Factors of 19704

List of positive integer factors of 19704 that divides 19688 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 821, 1642, 2463, 3284, 4926, 6568, 9852

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19688 and 19704. The biggest common factor number is the GCF number.
So the greatest common factor 19688 and 19704 is 8.

Also check out the Least Common Multiple of 19688 and 19704