What is the Greatest Common Factor of 21720 and 21735?

Greatest common factor (GCF) of 21720 and 21735 is 15.

GCF(21720,21735) = 15

We will now calculate the prime factors of 21720 and 21735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21720 and 21735.

How to find the GCF of 21720 and 21735?

We will first find the prime factorization of 21720 and 21735. After we will calculate the factors of 21720 and 21735 and find the biggest common factor number .

Step-1: Prime Factorization of 21720

Prime factors of 21720 are 2, 3, 5, 181. Prime factorization of 21720 in exponential form is:

21720 = 2³ × 3¹ × 5¹ × 181¹

Step-2: 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-3: Factors of 21720

List of positive integer factors of 21720 that divides 21720 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 181, 362, 543, 724, 905, 1086, 1448, 1810, 2172, 2715, 3620, 4344, 5430, 7240, 10860

Step-4: Factors of 21735

List of positive integer factors of 21735 that divides 21720 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21720 and 21735. The biggest common factor number is the GCF number.
So the greatest common factor 21720 and 21735 is 15.

Also check out the Least Common Multiple of 21720 and 21735