What is the Greatest Common Factor of 20784 and 20800?

Greatest common factor (GCF) of 20784 and 20800 is 16.

GCF(20784,20800) = 16

We will now calculate the prime factors of 20784 and 20800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20784 and 20800.

How to find the GCF of 20784 and 20800?

We will first find the prime factorization of 20784 and 20800. After we will calculate the factors of 20784 and 20800 and find the biggest common factor number .

Step-1: Prime Factorization of 20784

Prime factors of 20784 are 2, 3, 433. Prime factorization of 20784 in exponential form is:

20784 = 2⁴ × 3¹ × 433¹

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 20784

List of positive integer factors of 20784 that divides 20784 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 433, 866, 1299, 1732, 2598, 3464, 5196, 6928, 10392

Step-4: Factors of 20800

List of positive integer factors of 20800 that divides 20784 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 20784 and 20800. The biggest common factor number is the GCF number.
So the greatest common factor 20784 and 20800 is 16.

Also check out the Least Common Multiple of 20784 and 20800