What is the Greatest Common Factor of 19758 and 19773?

Greatest common factor (GCF) of 19758 and 19773 is 3.

GCF(19758,19773) = 3

We will now calculate the prime factors of 19758 and 19773, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19758 and 19773.

How to find the GCF of 19758 and 19773?

We will first find the prime factorization of 19758 and 19773. After we will calculate the factors of 19758 and 19773 and find the biggest common factor number .

Step-1: Prime Factorization of 19758

Prime factors of 19758 are 2, 3, 37, 89. Prime factorization of 19758 in exponential form is:

19758 = 2¹ × 3¹ × 37¹ × 89¹

Step-2: Prime Factorization of 19773

Prime factors of 19773 are 3, 13. Prime factorization of 19773 in exponential form is:

19773 = 3² × 13³

Step-3: Factors of 19758

List of positive integer factors of 19758 that divides 19758 without a remainder.

1, 2, 3, 6, 37, 74, 89, 111, 178, 222, 267, 534, 3293, 6586, 9879

Step-4: Factors of 19773

List of positive integer factors of 19773 that divides 19758 without a remainder.

1, 3, 9, 13, 39, 117, 169, 507, 1521, 2197, 6591

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19758 and 19773. The biggest common factor number is the GCF number.
So the greatest common factor 19758 and 19773 is 3.

Also check out the Least Common Multiple of 19758 and 19773