What is the Greatest Common Factor of 20785 and 20800?

Greatest common factor (GCF) of 20785 and 20800 is 5.

GCF(20785,20800) = 5

We will now calculate the prime factors of 20785 and 20800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20785 and 20800.

How to find the GCF of 20785 and 20800?

We will first find the prime factorization of 20785 and 20800. After we will calculate the factors of 20785 and 20800 and find the biggest common factor number .

Step-1: Prime Factorization of 20785

Prime factors of 20785 are 5, 4157. Prime factorization of 20785 in exponential form is:

20785 = 5¹ × 4157¹

Step-2: 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-3: Factors of 20785

List of positive integer factors of 20785 that divides 20785 without a remainder.

1, 5, 4157

Step-4: Factors of 20800

List of positive integer factors of 20800 that divides 20785 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20785 and 20800. The biggest common factor number is the GCF number.
So the greatest common factor 20785 and 20800 is 5.

Also check out the Least Common Multiple of 20785 and 20800