What is the Greatest Common Factor of 55305 and 55320?

Greatest common factor (GCF) of 55305 and 55320 is 15.

GCF(55305,55320) = 15

We will now calculate the prime factors of 55305 and 55320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 55305 and 55320.

How to find the GCF of 55305 and 55320?

We will first find the prime factorization of 55305 and 55320. After we will calculate the factors of 55305 and 55320 and find the biggest common factor number .

Step-1: Prime Factorization of 55305

Prime factors of 55305 are 3, 5, 1229. Prime factorization of 55305 in exponential form is:

55305 = 3² × 5¹ × 1229¹

Step-2: Prime Factorization of 55320

Prime factors of 55320 are 2, 3, 5, 461. Prime factorization of 55320 in exponential form is:

55320 = 2³ × 3¹ × 5¹ × 461¹

Step-3: Factors of 55305

List of positive integer factors of 55305 that divides 55305 without a remainder.

1, 3, 5, 9, 15, 45, 1229, 3687, 6145, 11061, 18435

Step-4: Factors of 55320

List of positive integer factors of 55320 that divides 55305 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 461, 922, 1383, 1844, 2305, 2766, 3688, 4610, 5532, 6915, 9220, 11064, 13830, 18440, 27660

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 55305 and 55320. The biggest common factor number is the GCF number.
So the greatest common factor 55305 and 55320 is 15.

Also check out the Least Common Multiple of 55305 and 55320