What is the Greatest Common Factor of 21854 and 21874?

Greatest common factor (GCF) of 21854 and 21874 is 2.

GCF(21854,21874) = 2

We will now calculate the prime factors of 21854 and 21874, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21854 and 21874.

How to find the GCF of 21854 and 21874?

We will first find the prime factorization of 21854 and 21874. After we will calculate the factors of 21854 and 21874 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 21874

Prime factors of 21874 are 2, 10937. Prime factorization of 21874 in exponential form is:

21874 = 2¹ × 10937¹

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 21874

List of positive integer factors of 21874 that divides 21854 without a remainder.

1, 2, 10937

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21854 and 21874. The biggest common factor number is the GCF number.
So the greatest common factor 21854 and 21874 is 2.

Also check out the Least Common Multiple of 21854 and 21874