What is the Greatest Common Factor of 21634 and 21649?

Greatest common factor (GCF) of 21634 and 21649 is 1.

GCF(21634,21649) = 1

We will now calculate the prime factors of 21634 and 21649, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21634 and 21649.

How to find the GCF of 21634 and 21649?

We will first find the prime factorization of 21634 and 21649. After we will calculate the factors of 21634 and 21649 and find the biggest common factor number .

Step-1: Prime Factorization of 21634

Prime factors of 21634 are 2, 29, 373. Prime factorization of 21634 in exponential form is:

21634 = 2¹ × 29¹ × 373¹

Step-2: Prime Factorization of 21649

Prime factors of 21649 are 21649. Prime factorization of 21649 in exponential form is:

21649 = 21649¹

Step-3: Factors of 21634

List of positive integer factors of 21634 that divides 21634 without a remainder.

1, 2, 29, 58, 373, 746, 10817

Step-4: Factors of 21649

List of positive integer factors of 21649 that divides 21634 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21634 and 21649. The biggest common factor number is the GCF number.
So the greatest common factor 21634 and 21649 is 1.

Also check out the Least Common Multiple of 21634 and 21649