What is the Greatest Common Factor of 21854 and 21864?

Greatest common factor (GCF) of 21854 and 21864 is 2.

GCF(21854,21864) = 2

We will now calculate the prime factors of 21854 and 21864, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21854 and 21864.

How to find the GCF of 21854 and 21864?

We will first find the prime factorization of 21854 and 21864. After we will calculate the factors of 21854 and 21864 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 21864

Prime factors of 21864 are 2, 3, 911. Prime factorization of 21864 in exponential form is:

21864 = 2³ × 3¹ × 911¹

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 21864

List of positive integer factors of 21864 that divides 21854 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 911, 1822, 2733, 3644, 5466, 7288, 10932

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21854 and 21864. The biggest common factor number is the GCF number.
So the greatest common factor 21854 and 21864 is 2.

Also check out the Least Common Multiple of 21854 and 21864