What is the Greatest Common Factor of 21404 and 21414?

Greatest common factor (GCF) of 21404 and 21414 is 2.

GCF(21404,21414) = 2

We will now calculate the prime factors of 21404 and 21414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21404 and 21414.

How to find the GCF of 21404 and 21414?

We will first find the prime factorization of 21404 and 21414. After we will calculate the factors of 21404 and 21414 and find the biggest common factor number .

Step-1: Prime Factorization of 21404

Prime factors of 21404 are 2, 5351. Prime factorization of 21404 in exponential form is:

21404 = 2² × 5351¹

Step-2: Prime Factorization of 21414

Prime factors of 21414 are 2, 3, 43, 83. Prime factorization of 21414 in exponential form is:

21414 = 2¹ × 3¹ × 43¹ × 83¹

Step-3: Factors of 21404

List of positive integer factors of 21404 that divides 21404 without a remainder.

1, 2, 4, 5351, 10702

Step-4: Factors of 21414

List of positive integer factors of 21414 that divides 21404 without a remainder.

1, 2, 3, 6, 43, 83, 86, 129, 166, 249, 258, 498, 3569, 7138, 10707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21404 and 21414. The biggest common factor number is the GCF number.
So the greatest common factor 21404 and 21414 is 2.

Also check out the Least Common Multiple of 21404 and 21414