What is the Greatest Common Factor of 21628 and 21648?

Greatest common factor (GCF) of 21628 and 21648 is 4.

GCF(21628,21648) = 4

We will now calculate the prime factors of 21628 and 21648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21628 and 21648.

How to find the GCF of 21628 and 21648?

We will first find the prime factorization of 21628 and 21648. After we will calculate the factors of 21628 and 21648 and find the biggest common factor number .

Step-1: Prime Factorization of 21628

Prime factors of 21628 are 2, 5407. Prime factorization of 21628 in exponential form is:

21628 = 2² × 5407¹

Step-2: Prime Factorization of 21648

Prime factors of 21648 are 2, 3, 11, 41. Prime factorization of 21648 in exponential form is:

21648 = 2⁴ × 3¹ × 11¹ × 41¹

Step-3: Factors of 21628

List of positive integer factors of 21628 that divides 21628 without a remainder.

1, 2, 4, 5407, 10814

Step-4: Factors of 21648

List of positive integer factors of 21648 that divides 21628 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 41, 44, 48, 66, 82, 88, 123, 132, 164, 176, 246, 264, 328, 451, 492, 528, 656, 902, 984, 1353, 1804, 1968, 2706, 3608, 5412, 7216, 10824

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21628 and 21648. The biggest common factor number is the GCF number.
So the greatest common factor 21628 and 21648 is 4.

Also check out the Least Common Multiple of 21628 and 21648