What is the Greatest Common Factor of 21854 and 21870?

Greatest common factor (GCF) of 21854 and 21870 is 2.

GCF(21854,21870) = 2

We will now calculate the prime factors of 21854 and 21870, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21854 and 21870.

How to find the GCF of 21854 and 21870?

We will first find the prime factorization of 21854 and 21870. After we will calculate the factors of 21854 and 21870 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 21870

Prime factors of 21870 are 2, 3, 5. Prime factorization of 21870 in exponential form is:

21870 = 2¹ × 3⁷ × 5¹

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 21870

List of positive integer factors of 21870 that divides 21854 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 729, 810, 1215, 1458, 2187, 2430, 3645, 4374, 7290, 10935

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21854 and 21870. The biggest common factor number is the GCF number.
So the greatest common factor 21854 and 21870 is 2.

Also check out the Least Common Multiple of 21854 and 21870