What is the Greatest Common Factor of 21392 and 21408?

Greatest common factor (GCF) of 21392 and 21408 is 16.

GCF(21392,21408) = 16

We will now calculate the prime factors of 21392 and 21408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21392 and 21408.

How to find the GCF of 21392 and 21408?

We will first find the prime factorization of 21392 and 21408. After we will calculate the factors of 21392 and 21408 and find the biggest common factor number .

Step-1: Prime Factorization of 21392

Prime factors of 21392 are 2, 7, 191. Prime factorization of 21392 in exponential form is:

21392 = 2⁴ × 7¹ × 191¹

Step-2: 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-3: Factors of 21392

List of positive integer factors of 21392 that divides 21392 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 191, 382, 764, 1337, 1528, 2674, 3056, 5348, 10696

Step-4: Factors of 21408

List of positive integer factors of 21408 that divides 21392 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21392 and 21408. The biggest common factor number is the GCF number.
So the greatest common factor 21392 and 21408 is 16.

Also check out the Least Common Multiple of 21392 and 21408