What is the Greatest Common Factor of 21854 and 21872?

Greatest common factor (GCF) of 21854 and 21872 is 2.

GCF(21854,21872) = 2

We will now calculate the prime factors of 21854 and 21872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21854 and 21872.

How to find the GCF of 21854 and 21872?

We will first find the prime factorization of 21854 and 21872. After we will calculate the factors of 21854 and 21872 and find the biggest common factor number .

Step-1: Prime Factorization of 21854

Prime factors of 21854 are 2, 7, 223. Prime factorization of 21854 in exponential form is:

21854 = 2¹ × 7² × 223¹

Step-2: Prime Factorization of 21872

Prime factors of 21872 are 2, 1367. Prime factorization of 21872 in exponential form is:

21872 = 2⁴ × 1367¹

Step-3: Factors of 21854

List of positive integer factors of 21854 that divides 21854 without a remainder.

1, 2, 7, 14, 49, 98, 223, 446, 1561, 3122, 10927

Step-4: Factors of 21872

List of positive integer factors of 21872 that divides 21854 without a remainder.

1, 2, 4, 8, 16, 1367, 2734, 5468, 10936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21854 and 21872. The biggest common factor number is the GCF number.
So the greatest common factor 21854 and 21872 is 2.

Also check out the Least Common Multiple of 21854 and 21872