What is the Greatest Common Factor of 21105 and 21120?

Greatest common factor (GCF) of 21105 and 21120 is 15.

GCF(21105,21120) = 15

We will now calculate the prime factors of 21105 and 21120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21105 and 21120.

How to find the GCF of 21105 and 21120?

We will first find the prime factorization of 21105 and 21120. After we will calculate the factors of 21105 and 21120 and find the biggest common factor number .

Step-1: Prime Factorization of 21105

Prime factors of 21105 are 3, 5, 7, 67. Prime factorization of 21105 in exponential form is:

21105 = 3² × 5¹ × 7¹ × 67¹

Step-2: Prime Factorization of 21120

Prime factors of 21120 are 2, 3, 5, 11. Prime factorization of 21120 in exponential form is:

21120 = 2⁷ × 3¹ × 5¹ × 11¹

Step-3: Factors of 21105

List of positive integer factors of 21105 that divides 21105 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 67, 105, 201, 315, 335, 469, 603, 1005, 1407, 2345, 3015, 4221, 7035

Step-4: Factors of 21120

List of positive integer factors of 21120 that divides 21105 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 64, 66, 80, 88, 96, 110, 120, 128, 132, 160, 165, 176, 192, 220, 240, 264, 320, 330, 352, 384, 440, 480, 528, 640, 660, 704, 880, 960, 1056, 1320, 1408, 1760, 1920, 2112, 2640, 3520, 4224, 5280, 7040, 10560

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21105 and 21120. The biggest common factor number is the GCF number.
So the greatest common factor 21105 and 21120 is 15.

Also check out the Least Common Multiple of 21105 and 21120