What is the Greatest Common Factor of 45305 and 45322?

Greatest common factor (GCF) of 45305 and 45322 is 17.

GCF(45305,45322) = 17

We will now calculate the prime factors of 45305 and 45322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45305 and 45322.

How to find the GCF of 45305 and 45322?

We will first find the prime factorization of 45305 and 45322. After we will calculate the factors of 45305 and 45322 and find the biggest common factor number .

Step-1: Prime Factorization of 45305

Prime factors of 45305 are 5, 13, 17, 41. Prime factorization of 45305 in exponential form is:

45305 = 5¹ × 13¹ × 17¹ × 41¹

Step-2: Prime Factorization of 45322

Prime factors of 45322 are 2, 17, 31, 43. Prime factorization of 45322 in exponential form is:

45322 = 2¹ × 17¹ × 31¹ × 43¹

Step-3: Factors of 45305

List of positive integer factors of 45305 that divides 45305 without a remainder.

1, 5, 13, 17, 41, 65, 85, 205, 221, 533, 697, 1105, 2665, 3485, 9061

Step-4: Factors of 45322

List of positive integer factors of 45322 that divides 45305 without a remainder.

1, 2, 17, 31, 34, 43, 62, 86, 527, 731, 1054, 1333, 1462, 2666, 22661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45305 and 45322. The biggest common factor number is the GCF number.
So the greatest common factor 45305 and 45322 is 17.

Also check out the Least Common Multiple of 45305 and 45322