What is the Greatest Common Factor of 21762 and 21775?

Greatest common factor (GCF) of 21762 and 21775 is 13.

GCF(21762,21775) = 13

We will now calculate the prime factors of 21762 and 21775, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21762 and 21775.

How to find the GCF of 21762 and 21775?

We will first find the prime factorization of 21762 and 21775. After we will calculate the factors of 21762 and 21775 and find the biggest common factor number .

Step-1: Prime Factorization of 21762

Prime factors of 21762 are 2, 3, 13, 31. Prime factorization of 21762 in exponential form is:

21762 = 2¹ × 3³ × 13¹ × 31¹

Step-2: Prime Factorization of 21775

Prime factors of 21775 are 5, 13, 67. Prime factorization of 21775 in exponential form is:

21775 = 5² × 13¹ × 67¹

Step-3: Factors of 21762

List of positive integer factors of 21762 that divides 21762 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 31, 39, 54, 62, 78, 93, 117, 186, 234, 279, 351, 403, 558, 702, 806, 837, 1209, 1674, 2418, 3627, 7254, 10881

Step-4: Factors of 21775

List of positive integer factors of 21775 that divides 21762 without a remainder.

1, 5, 13, 25, 65, 67, 325, 335, 871, 1675, 4355

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21762 and 21775. The biggest common factor number is the GCF number.
So the greatest common factor 21762 and 21775 is 13.

Also check out the Least Common Multiple of 21762 and 21775