What is the Greatest Common Factor of 15180 and 15200?

Greatest common factor (GCF) of 15180 and 15200 is 20.

GCF(15180,15200) = 20

We will now calculate the prime factors of 15180 and 15200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15180 and 15200.

How to find the GCF of 15180 and 15200?

We will first find the prime factorization of 15180 and 15200. After we will calculate the factors of 15180 and 15200 and find the biggest common factor number .

Step-1: Prime Factorization of 15180

Prime factors of 15180 are 2, 3, 5, 11, 23. Prime factorization of 15180 in exponential form is:

15180 = 2² × 3¹ × 5¹ × 11¹ × 23¹

Step-2: Prime Factorization of 15200

Prime factors of 15200 are 2, 5, 19. Prime factorization of 15200 in exponential form is:

15200 = 2⁵ × 5² × 19¹

Step-3: Factors of 15180

List of positive integer factors of 15180 that divides 15180 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 23, 30, 33, 44, 46, 55, 60, 66, 69, 92, 110, 115, 132, 138, 165, 220, 230, 253, 276, 330, 345, 460, 506, 660, 690, 759, 1012, 1265, 1380, 1518, 2530, 3036, 3795, 5060, 7590

Step-4: Factors of 15200

List of positive integer factors of 15200 that divides 15180 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 25, 32, 38, 40, 50, 76, 80, 95, 100, 152, 160, 190, 200, 304, 380, 400, 475, 608, 760, 800, 950, 1520, 1900, 3040, 3800, 7600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15180 and 15200. The biggest common factor number is the GCF number.
So the greatest common factor 15180 and 15200 is 20.

Also check out the Least Common Multiple of 15180 and 15200