What is the Greatest Common Factor of 21735 and 21750?

Greatest common factor (GCF) of 21735 and 21750 is 15.

GCF(21735,21750) = 15

We will now calculate the prime factors of 21735 and 21750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21735 and 21750.

How to find the GCF of 21735 and 21750?

We will first find the prime factorization of 21735 and 21750. After we will calculate the factors of 21735 and 21750 and find the biggest common factor number .

Step-1: Prime Factorization of 21735

Prime factors of 21735 are 3, 5, 7, 23. Prime factorization of 21735 in exponential form is:

21735 = 3³ × 5¹ × 7¹ × 23¹

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 21735

List of positive integer factors of 21735 that divides 21735 without a remainder.

1, 3, 5, 7, 9, 15, 21, 23, 27, 35, 45, 63, 69, 105, 115, 135, 161, 189, 207, 315, 345, 483, 621, 805, 945, 1035, 1449, 2415, 3105, 4347, 7245

Step-4: Factors of 21750

List of positive integer factors of 21750 that divides 21735 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 21735 and 21750. The biggest common factor number is the GCF number.
So the greatest common factor 21735 and 21750 is 15.

Also check out the Least Common Multiple of 21735 and 21750