What is the Greatest Common Factor of 21638 and 21652?

Greatest common factor (GCF) of 21638 and 21652 is 2.

GCF(21638,21652) = 2

We will now calculate the prime factors of 21638 and 21652, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21638 and 21652.

How to find the GCF of 21638 and 21652?

We will first find the prime factorization of 21638 and 21652. After we will calculate the factors of 21638 and 21652 and find the biggest common factor number .

Step-1: Prime Factorization of 21638

Prime factors of 21638 are 2, 31, 349. Prime factorization of 21638 in exponential form is:

21638 = 2¹ × 31¹ × 349¹

Step-2: Prime Factorization of 21652

Prime factors of 21652 are 2, 5413. Prime factorization of 21652 in exponential form is:

21652 = 2² × 5413¹

Step-3: Factors of 21638

List of positive integer factors of 21638 that divides 21638 without a remainder.

1, 2, 31, 62, 349, 698, 10819

Step-4: Factors of 21652

List of positive integer factors of 21652 that divides 21638 without a remainder.

1, 2, 4, 5413, 10826

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21638 and 21652. The biggest common factor number is the GCF number.
So the greatest common factor 21638 and 21652 is 2.

Also check out the Least Common Multiple of 21638 and 21652