What is the Greatest Common Factor of 21784 and 21800?

Greatest common factor (GCF) of 21784 and 21800 is 8.

GCF(21784,21800) = 8

We will now calculate the prime factors of 21784 and 21800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21784 and 21800.

How to find the GCF of 21784 and 21800?

We will first find the prime factorization of 21784 and 21800. After we will calculate the factors of 21784 and 21800 and find the biggest common factor number .

Step-1: Prime Factorization of 21784

Prime factors of 21784 are 2, 7, 389. Prime factorization of 21784 in exponential form is:

21784 = 2³ × 7¹ × 389¹

Step-2: Prime Factorization of 21800

Prime factors of 21800 are 2, 5, 109. Prime factorization of 21800 in exponential form is:

21800 = 2³ × 5² × 109¹

Step-3: Factors of 21784

List of positive integer factors of 21784 that divides 21784 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 389, 778, 1556, 2723, 3112, 5446, 10892

Step-4: Factors of 21800

List of positive integer factors of 21800 that divides 21784 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 109, 200, 218, 436, 545, 872, 1090, 2180, 2725, 4360, 5450, 10900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21784 and 21800. The biggest common factor number is the GCF number.
So the greatest common factor 21784 and 21800 is 8.

Also check out the Least Common Multiple of 21784 and 21800