What is the Greatest Common Factor of 37257 and 37275?

Greatest common factor (GCF) of 37257 and 37275 is 3.

GCF(37257,37275) = 3

We will now calculate the prime factors of 37257 and 37275, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37257 and 37275.

How to find the GCF of 37257 and 37275?

We will first find the prime factorization of 37257 and 37275. After we will calculate the factors of 37257 and 37275 and find the biggest common factor number .

Step-1: Prime Factorization of 37257

Prime factors of 37257 are 3, 11, 1129. Prime factorization of 37257 in exponential form is:

37257 = 3¹ × 11¹ × 1129¹

Step-2: Prime Factorization of 37275

Prime factors of 37275 are 3, 5, 7, 71. Prime factorization of 37275 in exponential form is:

37275 = 3¹ × 5² × 7¹ × 71¹

Step-3: Factors of 37257

List of positive integer factors of 37257 that divides 37257 without a remainder.

1, 3, 11, 33, 1129, 3387, 12419

Step-4: Factors of 37275

List of positive integer factors of 37275 that divides 37257 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 71, 75, 105, 175, 213, 355, 497, 525, 1065, 1491, 1775, 2485, 5325, 7455, 12425

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37257 and 37275. The biggest common factor number is the GCF number.
So the greatest common factor 37257 and 37275 is 3.

Also check out the Least Common Multiple of 37257 and 37275