What is the Greatest Common Factor of 21750 and 21766?

Greatest common factor (GCF) of 21750 and 21766 is 2.

GCF(21750,21766) = 2

We will now calculate the prime factors of 21750 and 21766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21750 and 21766.

How to find the GCF of 21750 and 21766?

We will first find the prime factorization of 21750 and 21766. After we will calculate the factors of 21750 and 21766 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21766

Prime factors of 21766 are 2, 10883. Prime factorization of 21766 in exponential form is:

21766 = 2¹ × 10883¹

Step-3: Factors of 21750

List of positive integer factors of 21750 that divides 21750 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

Step-4: Factors of 21766

List of positive integer factors of 21766 that divides 21750 without a remainder.

1, 2, 10883

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21750 and 21766. The biggest common factor number is the GCF number.
So the greatest common factor 21750 and 21766 is 2.

Also check out the Least Common Multiple of 21750 and 21766