What is the Greatest Common Factor of 21777 and 21784?

Greatest common factor (GCF) of 21777 and 21784 is 7.

GCF(21777,21784) = 7

We will now calculate the prime factors of 21777 and 21784, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21777 and 21784.

How to find the GCF of 21777 and 21784?

We will first find the prime factorization of 21777 and 21784. After we will calculate the factors of 21777 and 21784 and find the biggest common factor number .

Step-1: Prime Factorization of 21777

Prime factors of 21777 are 3, 7, 17, 61. Prime factorization of 21777 in exponential form is:

21777 = 3¹ × 7¹ × 17¹ × 61¹

Step-2: 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-3: Factors of 21777

List of positive integer factors of 21777 that divides 21777 without a remainder.

1, 3, 7, 17, 21, 51, 61, 119, 183, 357, 427, 1037, 1281, 3111, 7259

Step-4: Factors of 21784

List of positive integer factors of 21784 that divides 21777 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21777 and 21784. The biggest common factor number is the GCF number.
So the greatest common factor 21777 and 21784 is 7.

Also check out the Least Common Multiple of 21777 and 21784