What is the Greatest Common Factor of 38280 and 38300?

Greatest common factor (GCF) of 38280 and 38300 is 20.

GCF(38280,38300) = 20

We will now calculate the prime factors of 38280 and 38300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38280 and 38300.

How to find the GCF of 38280 and 38300?

We will first find the prime factorization of 38280 and 38300. After we will calculate the factors of 38280 and 38300 and find the biggest common factor number .

Step-1: Prime Factorization of 38280

Prime factors of 38280 are 2, 3, 5, 11, 29. Prime factorization of 38280 in exponential form is:

38280 = 2³ × 3¹ × 5¹ × 11¹ × 29¹

Step-2: Prime Factorization of 38300

Prime factors of 38300 are 2, 5, 383. Prime factorization of 38300 in exponential form is:

38300 = 2² × 5² × 383¹

Step-3: Factors of 38280

List of positive integer factors of 38280 that divides 38280 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 29, 30, 33, 40, 44, 55, 58, 60, 66, 87, 88, 110, 116, 120, 132, 145, 165, 174, 220, 232, 264, 290, 319, 330, 348, 435, 440, 580, 638, 660, 696, 870, 957, 1160, 1276, 1320, 1595, 1740, 1914, 2552, 3190, 3480, 3828, 4785, 6380, 7656, 9570, 12760, 19140

Step-4: Factors of 38300

List of positive integer factors of 38300 that divides 38280 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 383, 766, 1532, 1915, 3830, 7660, 9575, 19150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38280 and 38300. The biggest common factor number is the GCF number.
So the greatest common factor 38280 and 38300 is 20.

Also check out the Least Common Multiple of 38280 and 38300