What is the Greatest Common Factor of 55965 and 55980?

Greatest common factor (GCF) of 55965 and 55980 is 15.

GCF(55965,55980) = 15

We will now calculate the prime factors of 55965 and 55980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 55965 and 55980.

How to find the GCF of 55965 and 55980?

We will first find the prime factorization of 55965 and 55980. After we will calculate the factors of 55965 and 55980 and find the biggest common factor number .

Step-1: Prime Factorization of 55965

Prime factors of 55965 are 3, 5, 7, 13, 41. Prime factorization of 55965 in exponential form is:

55965 = 3¹ × 5¹ × 7¹ × 13¹ × 41¹

Step-2: Prime Factorization of 55980

Prime factors of 55980 are 2, 3, 5, 311. Prime factorization of 55980 in exponential form is:

55980 = 2² × 3² × 5¹ × 311¹

Step-3: Factors of 55965

List of positive integer factors of 55965 that divides 55965 without a remainder.

1, 3, 5, 7, 13, 15, 21, 35, 39, 41, 65, 91, 105, 123, 195, 205, 273, 287, 455, 533, 615, 861, 1365, 1435, 1599, 2665, 3731, 4305, 7995, 11193, 18655

Step-4: Factors of 55980

List of positive integer factors of 55980 that divides 55965 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 311, 622, 933, 1244, 1555, 1866, 2799, 3110, 3732, 4665, 5598, 6220, 9330, 11196, 13995, 18660, 27990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 55965 and 55980. The biggest common factor number is the GCF number.
So the greatest common factor 55965 and 55980 is 15.

Also check out the Least Common Multiple of 55965 and 55980