What is the Greatest Common Factor of 20500 and 20512?

Greatest common factor (GCF) of 20500 and 20512 is 4.

GCF(20500,20512) = 4

We will now calculate the prime factors of 20500 and 20512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20500 and 20512.

How to find the GCF of 20500 and 20512?

We will first find the prime factorization of 20500 and 20512. After we will calculate the factors of 20500 and 20512 and find the biggest common factor number .

Step-1: Prime Factorization of 20500

Prime factors of 20500 are 2, 5, 41. Prime factorization of 20500 in exponential form is:

20500 = 2² × 5³ × 41¹

Step-2: Prime Factorization of 20512

Prime factors of 20512 are 2, 641. Prime factorization of 20512 in exponential form is:

20512 = 2⁵ × 641¹

Step-3: Factors of 20500

List of positive integer factors of 20500 that divides 20500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 41, 50, 82, 100, 125, 164, 205, 250, 410, 500, 820, 1025, 2050, 4100, 5125, 10250

Step-4: Factors of 20512

List of positive integer factors of 20512 that divides 20500 without a remainder.

1, 2, 4, 8, 16, 32, 641, 1282, 2564, 5128, 10256

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20500 and 20512. The biggest common factor number is the GCF number.
So the greatest common factor 20500 and 20512 is 4.

Also check out the Least Common Multiple of 20500 and 20512