What is the Greatest Common Factor of 20800 and 20805?

Greatest common factor (GCF) of 20800 and 20805 is 5.

GCF(20800,20805) = 5

We will now calculate the prime factors of 20800 and 20805, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20800 and 20805.

How to find the GCF of 20800 and 20805?

We will first find the prime factorization of 20800 and 20805. After we will calculate the factors of 20800 and 20805 and find the biggest common factor number .

Step-1: Prime Factorization of 20800

Prime factors of 20800 are 2, 5, 13. Prime factorization of 20800 in exponential form is:

20800 = 2⁶ × 5² × 13¹

Step-2: Prime Factorization of 20805

Prime factors of 20805 are 3, 5, 19, 73. Prime factorization of 20805 in exponential form is:

20805 = 3¹ × 5¹ × 19¹ × 73¹

Step-3: Factors of 20800

List of positive integer factors of 20800 that divides 20800 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 64, 65, 80, 100, 104, 130, 160, 200, 208, 260, 320, 325, 400, 416, 520, 650, 800, 832, 1040, 1300, 1600, 2080, 2600, 4160, 5200, 10400

Step-4: Factors of 20805

List of positive integer factors of 20805 that divides 20800 without a remainder.

1, 3, 5, 15, 19, 57, 73, 95, 219, 285, 365, 1095, 1387, 4161, 6935

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20800 and 20805. The biggest common factor number is the GCF number.
So the greatest common factor 20800 and 20805 is 5.

Also check out the Least Common Multiple of 20800 and 20805