What is the Greatest Common Factor of 21854 and 21868?

Greatest common factor (GCF) of 21854 and 21868 is 14.

GCF(21854,21868) = 14

We will now calculate the prime factors of 21854 and 21868, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21854 and 21868.

How to find the GCF of 21854 and 21868?

We will first find the prime factorization of 21854 and 21868. After we will calculate the factors of 21854 and 21868 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 21868

Prime factors of 21868 are 2, 7, 11, 71. Prime factorization of 21868 in exponential form is:

21868 = 2² × 7¹ × 11¹ × 71¹

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 21868

List of positive integer factors of 21868 that divides 21854 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 71, 77, 142, 154, 284, 308, 497, 781, 994, 1562, 1988, 3124, 5467, 10934

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21854 and 21868. The biggest common factor number is the GCF number.
So the greatest common factor 21854 and 21868 is 14.

Also check out the Least Common Multiple of 21854 and 21868