What is the Greatest Common Factor of 19764 and 19770?

Greatest common factor (GCF) of 19764 and 19770 is 6.

GCF(19764,19770) = 6

We will now calculate the prime factors of 19764 and 19770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19764 and 19770.

How to find the GCF of 19764 and 19770?

We will first find the prime factorization of 19764 and 19770. After we will calculate the factors of 19764 and 19770 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 19770

Prime factors of 19770 are 2, 3, 5, 659. Prime factorization of 19770 in exponential form is:

19770 = 2¹ × 3¹ × 5¹ × 659¹

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 19770

List of positive integer factors of 19770 that divides 19764 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 659, 1318, 1977, 3295, 3954, 6590, 9885

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19764 and 19770. The biggest common factor number is the GCF number.
So the greatest common factor 19764 and 19770 is 6.

Also check out the Least Common Multiple of 19764 and 19770