What is the Greatest Common Factor of 19854 and 19872?

Greatest common factor (GCF) of 19854 and 19872 is 18.

GCF(19854,19872) = 18

We will now calculate the prime factors of 19854 and 19872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19854 and 19872.

How to find the GCF of 19854 and 19872?

We will first find the prime factorization of 19854 and 19872. After we will calculate the factors of 19854 and 19872 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19872

Prime factors of 19872 are 2, 3, 23. Prime factorization of 19872 in exponential form is:

19872 = 2⁵ × 3³ × 23¹

Step-3: Factors of 19854

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

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

Step-4: Factors of 19872

List of positive integer factors of 19872 that divides 19854 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 27, 32, 36, 46, 48, 54, 69, 72, 92, 96, 108, 138, 144, 184, 207, 216, 276, 288, 368, 414, 432, 552, 621, 736, 828, 864, 1104, 1242, 1656, 2208, 2484, 3312, 4968, 6624, 9936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19854 and 19872. The biggest common factor number is the GCF number.
So the greatest common factor 19854 and 19872 is 18.

Also check out the Least Common Multiple of 19854 and 19872