What is the Greatest Common Factor of 19729 and 19749?

Greatest common factor (GCF) of 19729 and 19749 is 1.

GCF(19729,19749) = 1

We will now calculate the prime factors of 19729 and 19749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19729 and 19749.

How to find the GCF of 19729 and 19749?

We will first find the prime factorization of 19729 and 19749. After we will calculate the factors of 19729 and 19749 and find the biggest common factor number .

Step-1: Prime Factorization of 19729

Prime factors of 19729 are 109, 181. Prime factorization of 19729 in exponential form is:

19729 = 109¹ × 181¹

Step-2: Prime Factorization of 19749

Prime factors of 19749 are 3, 29, 227. Prime factorization of 19749 in exponential form is:

19749 = 3¹ × 29¹ × 227¹

Step-3: Factors of 19729

List of positive integer factors of 19729 that divides 19729 without a remainder.

1, 109, 181

Step-4: Factors of 19749

List of positive integer factors of 19749 that divides 19729 without a remainder.

1, 3, 29, 87, 227, 681, 6583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19729 and 19749. The biggest common factor number is the GCF number.
So the greatest common factor 19729 and 19749 is 1.

Also check out the Least Common Multiple of 19729 and 19749