What is the Greatest Common Factor of 58905 and 58920?

Greatest common factor (GCF) of 58905 and 58920 is 15.

GCF(58905,58920) = 15

We will now calculate the prime factors of 58905 and 58920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58905 and 58920.

How to find the GCF of 58905 and 58920?

We will first find the prime factorization of 58905 and 58920. After we will calculate the factors of 58905 and 58920 and find the biggest common factor number .

Step-1: Prime Factorization of 58905

Prime factors of 58905 are 3, 5, 7, 11, 17. Prime factorization of 58905 in exponential form is:

58905 = 3² × 5¹ × 7¹ × 11¹ × 17¹

Step-2: Prime Factorization of 58920

Prime factors of 58920 are 2, 3, 5, 491. Prime factorization of 58920 in exponential form is:

58920 = 2³ × 3¹ × 5¹ × 491¹

Step-3: Factors of 58905

List of positive integer factors of 58905 that divides 58905 without a remainder.

1, 3, 5, 7, 9, 11, 15, 17, 21, 33, 35, 45, 51, 55, 63, 77, 85, 99, 105, 119, 153, 165, 187, 231, 255, 315, 357, 385, 495, 561, 595, 693, 765, 935, 1071, 1155, 1309, 1683, 1785, 2805, 3465, 3927, 5355, 6545, 8415, 11781, 19635

Step-4: Factors of 58920

List of positive integer factors of 58920 that divides 58905 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 491, 982, 1473, 1964, 2455, 2946, 3928, 4910, 5892, 7365, 9820, 11784, 14730, 19640, 29460

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58905 and 58920. The biggest common factor number is the GCF number.
So the greatest common factor 58905 and 58920 is 15.

Also check out the Least Common Multiple of 58905 and 58920