What is the Greatest Common Factor of 21408 and 21422?

Greatest common factor (GCF) of 21408 and 21422 is 2.

GCF(21408,21422) = 2

We will now calculate the prime factors of 21408 and 21422, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21408 and 21422.

How to find the GCF of 21408 and 21422?

We will first find the prime factorization of 21408 and 21422. After we will calculate the factors of 21408 and 21422 and find the biggest common factor number .

Step-1: Prime Factorization of 21408

Prime factors of 21408 are 2, 3, 223. Prime factorization of 21408 in exponential form is:

21408 = 2⁵ × 3¹ × 223¹

Step-2: Prime Factorization of 21422

Prime factors of 21422 are 2, 10711. Prime factorization of 21422 in exponential form is:

21422 = 2¹ × 10711¹

Step-3: Factors of 21408

List of positive integer factors of 21408 that divides 21408 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 223, 446, 669, 892, 1338, 1784, 2676, 3568, 5352, 7136, 10704

Step-4: Factors of 21422

List of positive integer factors of 21422 that divides 21408 without a remainder.

1, 2, 10711

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21408 and 21422. The biggest common factor number is the GCF number.
So the greatest common factor 21408 and 21422 is 2.

Also check out the Least Common Multiple of 21408 and 21422