What is the Greatest Common Factor of 19764 and 19780?

Greatest common factor (GCF) of 19764 and 19780 is 4.

GCF(19764,19780) = 4

We will now calculate the prime factors of 19764 and 19780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19764 and 19780.

How to find the GCF of 19764 and 19780?

We will first find the prime factorization of 19764 and 19780. After we will calculate the factors of 19764 and 19780 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19780

Prime factors of 19780 are 2, 5, 23, 43. Prime factorization of 19780 in exponential form is:

19780 = 2² × 5¹ × 23¹ × 43¹

Step-3: Factors of 19764

List of positive integer factors of 19764 that divides 19764 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

Step-4: Factors of 19780

List of positive integer factors of 19780 that divides 19764 without a remainder.

1, 2, 4, 5, 10, 20, 23, 43, 46, 86, 92, 115, 172, 215, 230, 430, 460, 860, 989, 1978, 3956, 4945, 9890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19764 and 19780. The biggest common factor number is the GCF number.
So the greatest common factor 19764 and 19780 is 4.

Also check out the Least Common Multiple of 19764 and 19780