What is the Greatest Common Factor of 37697 and 37714?

Greatest common factor (GCF) of 37697 and 37714 is 1.

GCF(37697,37714) = 1

We will now calculate the prime factors of 37697 and 37714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37697 and 37714.

How to find the GCF of 37697 and 37714?

We will first find the prime factorization of 37697 and 37714. After we will calculate the factors of 37697 and 37714 and find the biggest common factor number .

Step-1: Prime Factorization of 37697

Prime factors of 37697 are 11, 23, 149. Prime factorization of 37697 in exponential form is:

37697 = 11¹ × 23¹ × 149¹

Step-2: Prime Factorization of 37714

Prime factors of 37714 are 2, 109, 173. Prime factorization of 37714 in exponential form is:

37714 = 2¹ × 109¹ × 173¹

Step-3: Factors of 37697

List of positive integer factors of 37697 that divides 37697 without a remainder.

1, 11, 23, 149, 253, 1639, 3427

Step-4: Factors of 37714

List of positive integer factors of 37714 that divides 37697 without a remainder.

1, 2, 109, 173, 218, 346, 18857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37697 and 37714. The biggest common factor number is the GCF number.
So the greatest common factor 37697 and 37714 is 1.

Also check out the Least Common Multiple of 37697 and 37714