What is the Greatest Common Factor of 19749 and 19764?

Greatest common factor (GCF) of 19749 and 19764 is 3.

GCF(19749,19764) = 3

We will now calculate the prime factors of 19749 and 19764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19749 and 19764.

How to find the GCF of 19749 and 19764?

We will first find the prime factorization of 19749 and 19764. After we will calculate the factors of 19749 and 19764 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19764

Prime factors of 19764 are 2, 3, 61. Prime factorization of 19764 in exponential form is:

19764 = 2² × 3⁴ × 61¹

Step-3: Factors of 19749

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

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

Step-4: Factors of 19764

List of positive integer factors of 19764 that divides 19749 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 61, 81, 108, 122, 162, 183, 244, 324, 366, 549, 732, 1098, 1647, 2196, 3294, 4941, 6588, 9882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19749 and 19764. The biggest common factor number is the GCF number.
So the greatest common factor 19749 and 19764 is 3.

Also check out the Least Common Multiple of 19749 and 19764