What is the Greatest Common Factor of 19737 and 19749?

Greatest common factor (GCF) of 19737 and 19749 is 3.

GCF(19737,19749) = 3

We will now calculate the prime factors of 19737 and 19749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19737 and 19749.

How to find the GCF of 19737 and 19749?

We will first find the prime factorization of 19737 and 19749. After we will calculate the factors of 19737 and 19749 and find the biggest common factor number .

Step-1: Prime Factorization of 19737

Prime factors of 19737 are 3, 17, 43. Prime factorization of 19737 in exponential form is:

19737 = 3³ × 17¹ × 43¹

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 19737

List of positive integer factors of 19737 that divides 19737 without a remainder.

1, 3, 9, 17, 27, 43, 51, 129, 153, 387, 459, 731, 1161, 2193, 6579

Step-4: Factors of 19749

List of positive integer factors of 19749 that divides 19737 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19737 and 19749. The biggest common factor number is the GCF number.
So the greatest common factor 19737 and 19749 is 3.

Also check out the Least Common Multiple of 19737 and 19749