What is the Greatest Common Factor of 21745 and 21762?

Greatest common factor (GCF) of 21745 and 21762 is 1.

GCF(21745,21762) = 1

We will now calculate the prime factors of 21745 and 21762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21745 and 21762.

How to find the GCF of 21745 and 21762?

We will first find the prime factorization of 21745 and 21762. After we will calculate the factors of 21745 and 21762 and find the biggest common factor number .

Step-1: Prime Factorization of 21745

Prime factors of 21745 are 5, 4349. Prime factorization of 21745 in exponential form is:

21745 = 5¹ × 4349¹

Step-2: 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-3: Factors of 21745

List of positive integer factors of 21745 that divides 21745 without a remainder.

1, 5, 4349

Step-4: Factors of 21762

List of positive integer factors of 21762 that divides 21745 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21745 and 21762. The biggest common factor number is the GCF number.
So the greatest common factor 21745 and 21762 is 1.

Also check out the Least Common Multiple of 21745 and 21762