What is the Greatest Common Factor of 21842 and 21854?

Greatest common factor (GCF) of 21842 and 21854 is 2.

GCF(21842,21854) = 2

We will now calculate the prime factors of 21842 and 21854, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21842 and 21854.

How to find the GCF of 21842 and 21854?

We will first find the prime factorization of 21842 and 21854. After we will calculate the factors of 21842 and 21854 and find the biggest common factor number .

Step-1: Prime Factorization of 21842

Prime factors of 21842 are 2, 67, 163. Prime factorization of 21842 in exponential form is:

21842 = 2¹ × 67¹ × 163¹

Step-2: 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-3: Factors of 21842

List of positive integer factors of 21842 that divides 21842 without a remainder.

1, 2, 67, 134, 163, 326, 10921

Step-4: Factors of 21854

List of positive integer factors of 21854 that divides 21842 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21842 and 21854. The biggest common factor number is the GCF number.
So the greatest common factor 21842 and 21854 is 2.

Also check out the Least Common Multiple of 21842 and 21854