What is the Greatest Common Factor of 21697 and 21710?

Greatest common factor (GCF) of 21697 and 21710 is 13.

GCF(21697,21710) = 13

We will now calculate the prime factors of 21697 and 21710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21697 and 21710.

How to find the GCF of 21697 and 21710?

We will first find the prime factorization of 21697 and 21710. After we will calculate the factors of 21697 and 21710 and find the biggest common factor number .

Step-1: Prime Factorization of 21697

Prime factors of 21697 are 13, 1669. Prime factorization of 21697 in exponential form is:

21697 = 13¹ × 1669¹

Step-2: Prime Factorization of 21710

Prime factors of 21710 are 2, 5, 13, 167. Prime factorization of 21710 in exponential form is:

21710 = 2¹ × 5¹ × 13¹ × 167¹

Step-3: Factors of 21697

List of positive integer factors of 21697 that divides 21697 without a remainder.

1, 13, 1669

Step-4: Factors of 21710

List of positive integer factors of 21710 that divides 21697 without a remainder.

1, 2, 5, 10, 13, 26, 65, 130, 167, 334, 835, 1670, 2171, 4342, 10855

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21697 and 21710. The biggest common factor number is the GCF number.
So the greatest common factor 21697 and 21710 is 13.

Also check out the Least Common Multiple of 21697 and 21710