What is the Greatest Common Factor of 38100 and 38115?

Greatest common factor (GCF) of 38100 and 38115 is 15.

GCF(38100,38115) = 15

We will now calculate the prime factors of 38100 and 38115, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38100 and 38115.

How to find the GCF of 38100 and 38115?

We will first find the prime factorization of 38100 and 38115. After we will calculate the factors of 38100 and 38115 and find the biggest common factor number .

Step-1: Prime Factorization of 38100

Prime factors of 38100 are 2, 3, 5, 127. Prime factorization of 38100 in exponential form is:

38100 = 2² × 3¹ × 5² × 127¹

Step-2: Prime Factorization of 38115

Prime factors of 38115 are 3, 5, 7, 11. Prime factorization of 38115 in exponential form is:

38115 = 3² × 5¹ × 7¹ × 11²

Step-3: Factors of 38100

List of positive integer factors of 38100 that divides 38100 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 127, 150, 254, 300, 381, 508, 635, 762, 1270, 1524, 1905, 2540, 3175, 3810, 6350, 7620, 9525, 12700, 19050

Step-4: Factors of 38115

List of positive integer factors of 38115 that divides 38100 without a remainder.

1, 3, 5, 7, 9, 11, 15, 21, 33, 35, 45, 55, 63, 77, 99, 105, 121, 165, 231, 315, 363, 385, 495, 605, 693, 847, 1089, 1155, 1815, 2541, 3465, 4235, 5445, 7623, 12705

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38100 and 38115. The biggest common factor number is the GCF number.
So the greatest common factor 38100 and 38115 is 15.

Also check out the Least Common Multiple of 38100 and 38115