What is the Greatest Common Factor of 19688 and 19706?

Greatest common factor (GCF) of 19688 and 19706 is 2.

GCF(19688,19706) = 2

We will now calculate the prime factors of 19688 and 19706, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19688 and 19706.

How to find the GCF of 19688 and 19706?

We will first find the prime factorization of 19688 and 19706. After we will calculate the factors of 19688 and 19706 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 19706

Prime factors of 19706 are 2, 59, 167. Prime factorization of 19706 in exponential form is:

19706 = 2¹ × 59¹ × 167¹

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 19706

List of positive integer factors of 19706 that divides 19688 without a remainder.

1, 2, 59, 118, 167, 334, 9853

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19688 and 19706. The biggest common factor number is the GCF number.
So the greatest common factor 19688 and 19706 is 2.

Also check out the Least Common Multiple of 19688 and 19706