What is the Greatest Common Factor of 37671 and 37680?

Greatest common factor (GCF) of 37671 and 37680 is 3.

GCF(37671,37680) = 3

We will now calculate the prime factors of 37671 and 37680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37671 and 37680.

How to find the GCF of 37671 and 37680?

We will first find the prime factorization of 37671 and 37680. After we will calculate the factors of 37671 and 37680 and find the biggest common factor number .

Step-1: Prime Factorization of 37671

Prime factors of 37671 are 3, 29, 433. Prime factorization of 37671 in exponential form is:

37671 = 3¹ × 29¹ × 433¹

Step-2: Prime Factorization of 37680

Prime factors of 37680 are 2, 3, 5, 157. Prime factorization of 37680 in exponential form is:

37680 = 2⁴ × 3¹ × 5¹ × 157¹

Step-3: Factors of 37671

List of positive integer factors of 37671 that divides 37671 without a remainder.

1, 3, 29, 87, 433, 1299, 12557

Step-4: Factors of 37680

List of positive integer factors of 37680 that divides 37671 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 157, 240, 314, 471, 628, 785, 942, 1256, 1570, 1884, 2355, 2512, 3140, 3768, 4710, 6280, 7536, 9420, 12560, 18840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37671 and 37680. The biggest common factor number is the GCF number.
So the greatest common factor 37671 and 37680 is 3.

Also check out the Least Common Multiple of 37671 and 37680