What is the Greatest Common Factor of 37680 and 37686?

Greatest common factor (GCF) of 37680 and 37686 is 6.

GCF(37680,37686) = 6

We will now calculate the prime factors of 37680 and 37686, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37680 and 37686.

How to find the GCF of 37680 and 37686?

We will first find the prime factorization of 37680 and 37686. After we will calculate the factors of 37680 and 37686 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 37686

Prime factors of 37686 are 2, 3, 11, 571. Prime factorization of 37686 in exponential form is:

37686 = 2¹ × 3¹ × 11¹ × 571¹

Step-3: Factors of 37680

List of positive integer factors of 37680 that divides 37680 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

Step-4: Factors of 37686

List of positive integer factors of 37686 that divides 37680 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 571, 1142, 1713, 3426, 6281, 12562, 18843

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37680 and 37686. The biggest common factor number is the GCF number.
So the greatest common factor 37680 and 37686 is 6.

Also check out the Least Common Multiple of 37680 and 37686