What is the Greatest Common Factor of 19814 and 19822?

Greatest common factor (GCF) of 19814 and 19822 is 2.

GCF(19814,19822) = 2

We will now calculate the prime factors of 19814 and 19822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19814 and 19822.

How to find the GCF of 19814 and 19822?

We will first find the prime factorization of 19814 and 19822. After we will calculate the factors of 19814 and 19822 and find the biggest common factor number .

Step-1: Prime Factorization of 19814

Prime factors of 19814 are 2, 9907. Prime factorization of 19814 in exponential form is:

19814 = 2¹ × 9907¹

Step-2: Prime Factorization of 19822

Prime factors of 19822 are 2, 11, 17, 53. Prime factorization of 19822 in exponential form is:

19822 = 2¹ × 11¹ × 17¹ × 53¹

Step-3: Factors of 19814

List of positive integer factors of 19814 that divides 19814 without a remainder.

1, 2, 9907

Step-4: Factors of 19822

List of positive integer factors of 19822 that divides 19814 without a remainder.

1, 2, 11, 17, 22, 34, 53, 106, 187, 374, 583, 901, 1166, 1802, 9911

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19814 and 19822. The biggest common factor number is the GCF number.
So the greatest common factor 19814 and 19822 is 2.

Also check out the Least Common Multiple of 19814 and 19822