What is the Greatest Common Factor of 21645 and 21658?

Greatest common factor (GCF) of 21645 and 21658 is 13.

GCF(21645,21658) = 13

We will now calculate the prime factors of 21645 and 21658, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21645 and 21658.

How to find the GCF of 21645 and 21658?

We will first find the prime factorization of 21645 and 21658. After we will calculate the factors of 21645 and 21658 and find the biggest common factor number .

Step-1: Prime Factorization of 21645

Prime factors of 21645 are 3, 5, 13, 37. Prime factorization of 21645 in exponential form is:

21645 = 3² × 5¹ × 13¹ × 37¹

Step-2: Prime Factorization of 21658

Prime factors of 21658 are 2, 7, 13, 17. Prime factorization of 21658 in exponential form is:

21658 = 2¹ × 7² × 13¹ × 17¹

Step-3: Factors of 21645

List of positive integer factors of 21645 that divides 21645 without a remainder.

1, 3, 5, 9, 13, 15, 37, 39, 45, 65, 111, 117, 185, 195, 333, 481, 555, 585, 1443, 1665, 2405, 4329, 7215

Step-4: Factors of 21658

List of positive integer factors of 21658 that divides 21645 without a remainder.

1, 2, 7, 13, 14, 17, 26, 34, 49, 91, 98, 119, 182, 221, 238, 442, 637, 833, 1274, 1547, 1666, 3094, 10829

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21645 and 21658. The biggest common factor number is the GCF number.
So the greatest common factor 21645 and 21658 is 13.

Also check out the Least Common Multiple of 21645 and 21658