What is the Greatest Common Factor of 19760 and 19774?

Greatest common factor (GCF) of 19760 and 19774 is 2.

GCF(19760,19774) = 2

We will now calculate the prime factors of 19760 and 19774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19760 and 19774.

How to find the GCF of 19760 and 19774?

We will first find the prime factorization of 19760 and 19774. After we will calculate the factors of 19760 and 19774 and find the biggest common factor number .

Step-1: Prime Factorization of 19760

Prime factors of 19760 are 2, 5, 13, 19. Prime factorization of 19760 in exponential form is:

19760 = 2⁴ × 5¹ × 13¹ × 19¹

Step-2: Prime Factorization of 19774

Prime factors of 19774 are 2, 9887. Prime factorization of 19774 in exponential form is:

19774 = 2¹ × 9887¹

Step-3: Factors of 19760

List of positive integer factors of 19760 that divides 19760 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 19, 20, 26, 38, 40, 52, 65, 76, 80, 95, 104, 130, 152, 190, 208, 247, 260, 304, 380, 494, 520, 760, 988, 1040, 1235, 1520, 1976, 2470, 3952, 4940, 9880

Step-4: Factors of 19774

List of positive integer factors of 19774 that divides 19760 without a remainder.

1, 2, 9887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19760 and 19774. The biggest common factor number is the GCF number.
So the greatest common factor 19760 and 19774 is 2.

Also check out the Least Common Multiple of 19760 and 19774