What is the Greatest Common Factor of 21710 and 21730?

Greatest common factor (GCF) of 21710 and 21730 is 10.

GCF(21710,21730) = 10

We will now calculate the prime factors of 21710 and 21730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21710 and 21730.

How to find the GCF of 21710 and 21730?

We will first find the prime factorization of 21710 and 21730. After we will calculate the factors of 21710 and 21730 and find the biggest common factor number .

Step-1: Prime Factorization of 21710

Prime factors of 21710 are 2, 5, 13, 167. Prime factorization of 21710 in exponential form is:

21710 = 2¹ × 5¹ × 13¹ × 167¹

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 21710

List of positive integer factors of 21710 that divides 21710 without a remainder.

1, 2, 5, 10, 13, 26, 65, 130, 167, 334, 835, 1670, 2171, 4342, 10855

Step-4: Factors of 21730

List of positive integer factors of 21730 that divides 21710 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 21710 and 21730. The biggest common factor number is the GCF number.
So the greatest common factor 21710 and 21730 is 10.

Also check out the Least Common Multiple of 21710 and 21730