What is the Greatest Common Factor of 37065 and 37072?

Greatest common factor (GCF) of 37065 and 37072 is 7.

GCF(37065,37072) = 7

We will now calculate the prime factors of 37065 and 37072, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37065 and 37072.

How to find the GCF of 37065 and 37072?

We will first find the prime factorization of 37065 and 37072. After we will calculate the factors of 37065 and 37072 and find the biggest common factor number .

Step-1: Prime Factorization of 37065

Prime factors of 37065 are 3, 5, 7, 353. Prime factorization of 37065 in exponential form is:

37065 = 3¹ × 5¹ × 7¹ × 353¹

Step-2: Prime Factorization of 37072

Prime factors of 37072 are 2, 7, 331. Prime factorization of 37072 in exponential form is:

37072 = 2⁴ × 7¹ × 331¹

Step-3: Factors of 37065

List of positive integer factors of 37065 that divides 37065 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 353, 1059, 1765, 2471, 5295, 7413, 12355

Step-4: Factors of 37072

List of positive integer factors of 37072 that divides 37065 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 331, 662, 1324, 2317, 2648, 4634, 5296, 9268, 18536

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37065 and 37072. The biggest common factor number is the GCF number.
So the greatest common factor 37065 and 37072 is 7.

Also check out the Least Common Multiple of 37065 and 37072