What is the Greatest Common Factor of 37686 and 37706?

Greatest common factor (GCF) of 37686 and 37706 is 2.

GCF(37686,37706) = 2

We will now calculate the prime factors of 37686 and 37706, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37686 and 37706.

How to find the GCF of 37686 and 37706?

We will first find the prime factorization of 37686 and 37706. After we will calculate the factors of 37686 and 37706 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 37706

Prime factors of 37706 are 2, 17, 1109. Prime factorization of 37706 in exponential form is:

37706 = 2¹ × 17¹ × 1109¹

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 37706

List of positive integer factors of 37706 that divides 37686 without a remainder.

1, 2, 17, 34, 1109, 2218, 18853

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37686 and 37706. The biggest common factor number is the GCF number.
So the greatest common factor 37686 and 37706 is 2.

Also check out the Least Common Multiple of 37686 and 37706