What is the Greatest Common Factor of 37686 and 37704?

Greatest common factor (GCF) of 37686 and 37704 is 6.

GCF(37686,37704) = 6

We will now calculate the prime factors of 37686 and 37704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37686 and 37704.

How to find the GCF of 37686 and 37704?

We will first find the prime factorization of 37686 and 37704. After we will calculate the factors of 37686 and 37704 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 37704

Prime factors of 37704 are 2, 3, 1571. Prime factorization of 37704 in exponential form is:

37704 = 2³ × 3¹ × 1571¹

Step-3: Factors of 37686

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

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

Step-4: Factors of 37704

List of positive integer factors of 37704 that divides 37686 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1571, 3142, 4713, 6284, 9426, 12568, 18852

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37686 and 37704. The biggest common factor number is the GCF number.
So the greatest common factor 37686 and 37704 is 6.

Also check out the Least Common Multiple of 37686 and 37704