What is the Greatest Common Factor of 19838 and 19854?

Greatest common factor (GCF) of 19838 and 19854 is 2.

GCF(19838,19854) = 2

We will now calculate the prime factors of 19838 and 19854, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19838 and 19854.

How to find the GCF of 19838 and 19854?

We will first find the prime factorization of 19838 and 19854. After we will calculate the factors of 19838 and 19854 and find the biggest common factor number .

Step-1: Prime Factorization of 19838

Prime factors of 19838 are 2, 7, 13, 109. Prime factorization of 19838 in exponential form is:

19838 = 2¹ × 7¹ × 13¹ × 109¹

Step-2: Prime Factorization of 19854

Prime factors of 19854 are 2, 3, 1103. Prime factorization of 19854 in exponential form is:

19854 = 2¹ × 3² × 1103¹

Step-3: Factors of 19838

List of positive integer factors of 19838 that divides 19838 without a remainder.

1, 2, 7, 13, 14, 26, 91, 109, 182, 218, 763, 1417, 1526, 2834, 9919

Step-4: Factors of 19854

List of positive integer factors of 19854 that divides 19838 without a remainder.

1, 2, 3, 6, 9, 18, 1103, 2206, 3309, 6618, 9927

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19838 and 19854. The biggest common factor number is the GCF number.
So the greatest common factor 19838 and 19854 is 2.

Also check out the Least Common Multiple of 19838 and 19854