What is the Greatest Common Factor of 19726 and 19744?

Greatest common factor (GCF) of 19726 and 19744 is 2.

GCF(19726,19744) = 2

We will now calculate the prime factors of 19726 and 19744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19726 and 19744.

How to find the GCF of 19726 and 19744?

We will first find the prime factorization of 19726 and 19744. After we will calculate the factors of 19726 and 19744 and find the biggest common factor number .

Step-1: Prime Factorization of 19726

Prime factors of 19726 are 2, 7, 1409. Prime factorization of 19726 in exponential form is:

19726 = 2¹ × 7¹ × 1409¹

Step-2: Prime Factorization of 19744

Prime factors of 19744 are 2, 617. Prime factorization of 19744 in exponential form is:

19744 = 2⁵ × 617¹

Step-3: Factors of 19726

List of positive integer factors of 19726 that divides 19726 without a remainder.

1, 2, 7, 14, 1409, 2818, 9863

Step-4: Factors of 19744

List of positive integer factors of 19744 that divides 19726 without a remainder.

1, 2, 4, 8, 16, 32, 617, 1234, 2468, 4936, 9872

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19726 and 19744. The biggest common factor number is the GCF number.
So the greatest common factor 19726 and 19744 is 2.

Also check out the Least Common Multiple of 19726 and 19744