What is the Greatest Common Factor of 37275 and 37284?

Greatest common factor (GCF) of 37275 and 37284 is 3.

GCF(37275,37284) = 3

We will now calculate the prime factors of 37275 and 37284, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37275 and 37284.

How to find the GCF of 37275 and 37284?

We will first find the prime factorization of 37275 and 37284. After we will calculate the factors of 37275 and 37284 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 37284

Prime factors of 37284 are 2, 3, 13, 239. Prime factorization of 37284 in exponential form is:

37284 = 2² × 3¹ × 13¹ × 239¹

Step-3: Factors of 37275

List of positive integer factors of 37275 that divides 37275 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

Step-4: Factors of 37284

List of positive integer factors of 37284 that divides 37275 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 239, 478, 717, 956, 1434, 2868, 3107, 6214, 9321, 12428, 18642

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37275 and 37284. The biggest common factor number is the GCF number.
So the greatest common factor 37275 and 37284 is 3.

Also check out the Least Common Multiple of 37275 and 37284