What is the Greatest Common Factor of 21505 and 21522?

Greatest common factor (GCF) of 21505 and 21522 is 17.

GCF(21505,21522) = 17

We will now calculate the prime factors of 21505 and 21522, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21505 and 21522.

How to find the GCF of 21505 and 21522?

We will first find the prime factorization of 21505 and 21522. After we will calculate the factors of 21505 and 21522 and find the biggest common factor number .

Step-1: Prime Factorization of 21505

Prime factors of 21505 are 5, 11, 17, 23. Prime factorization of 21505 in exponential form is:

21505 = 5¹ × 11¹ × 17¹ × 23¹

Step-2: Prime Factorization of 21522

Prime factors of 21522 are 2, 3, 17, 211. Prime factorization of 21522 in exponential form is:

21522 = 2¹ × 3¹ × 17¹ × 211¹

Step-3: Factors of 21505

List of positive integer factors of 21505 that divides 21505 without a remainder.

1, 5, 11, 17, 23, 55, 85, 115, 187, 253, 391, 935, 1265, 1955, 4301

Step-4: Factors of 21522

List of positive integer factors of 21522 that divides 21505 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 211, 422, 633, 1266, 3587, 7174, 10761

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21505 and 21522. The biggest common factor number is the GCF number.
So the greatest common factor 21505 and 21522 is 17.

Also check out the Least Common Multiple of 21505 and 21522