What is the Greatest Common Factor of 21730 and 21750?

Greatest common factor (GCF) of 21730 and 21750 is 10.

GCF(21730,21750) = 10

We will now calculate the prime factors of 21730 and 21750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21730 and 21750.

How to find the GCF of 21730 and 21750?

We will first find the prime factorization of 21730 and 21750. After we will calculate the factors of 21730 and 21750 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21750

Prime factors of 21750 are 2, 3, 5, 29. Prime factorization of 21750 in exponential form is:

21750 = 2¹ × 3¹ × 5³ × 29¹

Step-3: Factors of 21730

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

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

Step-4: Factors of 21750

List of positive integer factors of 21750 that divides 21730 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 29, 30, 50, 58, 75, 87, 125, 145, 150, 174, 250, 290, 375, 435, 725, 750, 870, 1450, 2175, 3625, 4350, 7250, 10875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21730 and 21750. The biggest common factor number is the GCF number.
So the greatest common factor 21730 and 21750 is 10.

Also check out the Least Common Multiple of 21730 and 21750