What is the Greatest Common Factor of 20608 and 20624?

Greatest common factor (GCF) of 20608 and 20624 is 16.

GCF(20608,20624) = 16

We will now calculate the prime factors of 20608 and 20624, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20608 and 20624.

How to find the GCF of 20608 and 20624?

We will first find the prime factorization of 20608 and 20624. After we will calculate the factors of 20608 and 20624 and find the biggest common factor number .

Step-1: Prime Factorization of 20608

Prime factors of 20608 are 2, 7, 23. Prime factorization of 20608 in exponential form is:

20608 = 2⁷ × 7¹ × 23¹

Step-2: Prime Factorization of 20624

Prime factors of 20624 are 2, 1289. Prime factorization of 20624 in exponential form is:

20624 = 2⁴ × 1289¹

Step-3: Factors of 20608

List of positive integer factors of 20608 that divides 20608 without a remainder.

1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 56, 64, 92, 112, 128, 161, 184, 224, 322, 368, 448, 644, 736, 896, 1288, 1472, 2576, 2944, 5152, 10304

Step-4: Factors of 20624

List of positive integer factors of 20624 that divides 20608 without a remainder.

1, 2, 4, 8, 16, 1289, 2578, 5156, 10312

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20608 and 20624. The biggest common factor number is the GCF number.
So the greatest common factor 20608 and 20624 is 16.

Also check out the Least Common Multiple of 20608 and 20624