What is the Greatest Common Factor of 37200 and 37215?

Greatest common factor (GCF) of 37200 and 37215 is 15.

GCF(37200,37215) = 15

We will now calculate the prime factors of 37200 and 37215, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37200 and 37215.

How to find the GCF of 37200 and 37215?

We will first find the prime factorization of 37200 and 37215. After we will calculate the factors of 37200 and 37215 and find the biggest common factor number .

Step-1: Prime Factorization of 37200

Prime factors of 37200 are 2, 3, 5, 31. Prime factorization of 37200 in exponential form is:

37200 = 2⁴ × 3¹ × 5² × 31¹

Step-2: Prime Factorization of 37215

Prime factors of 37215 are 3, 5, 827. Prime factorization of 37215 in exponential form is:

37215 = 3² × 5¹ × 827¹

Step-3: Factors of 37200

List of positive integer factors of 37200 that divides 37200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 31, 40, 48, 50, 60, 62, 75, 80, 93, 100, 120, 124, 150, 155, 186, 200, 240, 248, 300, 310, 372, 400, 465, 496, 600, 620, 744, 775, 930, 1200, 1240, 1488, 1550, 1860, 2325, 2480, 3100, 3720, 4650, 6200, 7440, 9300, 12400, 18600

Step-4: Factors of 37215

List of positive integer factors of 37215 that divides 37200 without a remainder.

1, 3, 5, 9, 15, 45, 827, 2481, 4135, 7443, 12405

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37200 and 37215. The biggest common factor number is the GCF number.
So the greatest common factor 37200 and 37215 is 15.

Also check out the Least Common Multiple of 37200 and 37215