What is the Greatest Common Factor of 37365 and 37380?

Greatest common factor (GCF) of 37365 and 37380 is 15.

GCF(37365,37380) = 15

We will now calculate the prime factors of 37365 and 37380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37365 and 37380.

How to find the GCF of 37365 and 37380?

We will first find the prime factorization of 37365 and 37380. After we will calculate the factors of 37365 and 37380 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 37380

Prime factors of 37380 are 2, 3, 5, 7, 89. Prime factorization of 37380 in exponential form is:

37380 = 2² × 3¹ × 5¹ × 7¹ × 89¹

Step-3: Factors of 37365

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

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

Step-4: Factors of 37380

List of positive integer factors of 37380 that divides 37365 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 89, 105, 140, 178, 210, 267, 356, 420, 445, 534, 623, 890, 1068, 1246, 1335, 1780, 1869, 2492, 2670, 3115, 3738, 5340, 6230, 7476, 9345, 12460, 18690

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37365 and 37380. The biggest common factor number is the GCF number.
So the greatest common factor 37365 and 37380 is 15.

Also check out the Least Common Multiple of 37365 and 37380