What is the Greatest Common Factor of 21632 and 21645?

Greatest common factor (GCF) of 21632 and 21645 is 13.

GCF(21632,21645) = 13

We will now calculate the prime factors of 21632 and 21645, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21632 and 21645.

How to find the GCF of 21632 and 21645?

We will first find the prime factorization of 21632 and 21645. After we will calculate the factors of 21632 and 21645 and find the biggest common factor number .

Step-1: Prime Factorization of 21632

Prime factors of 21632 are 2, 13. Prime factorization of 21632 in exponential form is:

21632 = 2⁷ × 13²

Step-2: Prime Factorization of 21645

Prime factors of 21645 are 3, 5, 13, 37. Prime factorization of 21645 in exponential form is:

21645 = 3² × 5¹ × 13¹ × 37¹

Step-3: Factors of 21632

List of positive integer factors of 21632 that divides 21632 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 169, 208, 338, 416, 676, 832, 1352, 1664, 2704, 5408, 10816

Step-4: Factors of 21645

List of positive integer factors of 21645 that divides 21632 without a remainder.

1, 3, 5, 9, 13, 15, 37, 39, 45, 65, 111, 117, 185, 195, 333, 481, 555, 585, 1443, 1665, 2405, 4329, 7215

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21632 and 21645. The biggest common factor number is the GCF number.
So the greatest common factor 21632 and 21645 is 13.

Also check out the Least Common Multiple of 21632 and 21645