What is the Greatest Common Factor of 21297 and 21314?

Greatest common factor (GCF) of 21297 and 21314 is 1.

GCF(21297,21314) = 1

We will now calculate the prime factors of 21297 and 21314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21297 and 21314.

How to find the GCF of 21297 and 21314?

We will first find the prime factorization of 21297 and 21314. After we will calculate the factors of 21297 and 21314 and find the biggest common factor number .

Step-1: Prime Factorization of 21297

Prime factors of 21297 are 3, 31, 229. Prime factorization of 21297 in exponential form is:

21297 = 3¹ × 31¹ × 229¹

Step-2: Prime Factorization of 21314

Prime factors of 21314 are 2, 10657. Prime factorization of 21314 in exponential form is:

21314 = 2¹ × 10657¹

Step-3: Factors of 21297

List of positive integer factors of 21297 that divides 21297 without a remainder.

1, 3, 31, 93, 229, 687, 7099

Step-4: Factors of 21314

List of positive integer factors of 21314 that divides 21297 without a remainder.

1, 2, 10657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21297 and 21314. The biggest common factor number is the GCF number.
So the greatest common factor 21297 and 21314 is 1.

Also check out the Least Common Multiple of 21297 and 21314