What is the Greatest Common Factor of 21724 and 21730?

Greatest common factor (GCF) of 21724 and 21730 is 2.

GCF(21724,21730) = 2

We will now calculate the prime factors of 21724 and 21730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21724 and 21730.

How to find the GCF of 21724 and 21730?

We will first find the prime factorization of 21724 and 21730. After we will calculate the factors of 21724 and 21730 and find the biggest common factor number .

Step-1: Prime Factorization of 21724

Prime factors of 21724 are 2, 5431. Prime factorization of 21724 in exponential form is:

21724 = 2² × 5431¹

Step-2: Prime Factorization of 21730

Prime factors of 21730 are 2, 5, 41, 53. Prime factorization of 21730 in exponential form is:

21730 = 2¹ × 5¹ × 41¹ × 53¹

Step-3: Factors of 21724

List of positive integer factors of 21724 that divides 21724 without a remainder.

1, 2, 4, 5431, 10862

Step-4: Factors of 21730

List of positive integer factors of 21730 that divides 21724 without a remainder.

1, 2, 5, 10, 41, 53, 82, 106, 205, 265, 410, 530, 2173, 4346, 10865

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21724 and 21730. The biggest common factor number is the GCF number.
So the greatest common factor 21724 and 21730 is 2.

Also check out the Least Common Multiple of 21724 and 21730