What is the Greatest Common Factor of 37350 and 37365?

Greatest common factor (GCF) of 37350 and 37365 is 15.

GCF(37350,37365) = 15

We will now calculate the prime factors of 37350 and 37365, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37350 and 37365.

How to find the GCF of 37350 and 37365?

We will first find the prime factorization of 37350 and 37365. After we will calculate the factors of 37350 and 37365 and find the biggest common factor number .

Step-1: Prime Factorization of 37350

Prime factors of 37350 are 2, 3, 5, 83. Prime factorization of 37350 in exponential form is:

37350 = 2¹ × 3² × 5² × 83¹

Step-2: Prime Factorization of 37365

Prime factors of 37365 are 3, 5, 47, 53. Prime factorization of 37365 in exponential form is:

37365 = 3¹ × 5¹ × 47¹ × 53¹

Step-3: Factors of 37350

List of positive integer factors of 37350 that divides 37350 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 83, 90, 150, 166, 225, 249, 415, 450, 498, 747, 830, 1245, 1494, 2075, 2490, 3735, 4150, 6225, 7470, 12450, 18675

Step-4: Factors of 37365

List of positive integer factors of 37365 that divides 37350 without a remainder.

1, 3, 5, 15, 47, 53, 141, 159, 235, 265, 705, 795, 2491, 7473, 12455

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37350 and 37365. The biggest common factor number is the GCF number.
So the greatest common factor 37350 and 37365 is 15.

Also check out the Least Common Multiple of 37350 and 37365