What is the Greatest Common Factor of 37697 and 37708?

Greatest common factor (GCF) of 37697 and 37708 is 11.

GCF(37697,37708) = 11

We will now calculate the prime factors of 37697 and 37708, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37697 and 37708.

How to find the GCF of 37697 and 37708?

We will first find the prime factorization of 37697 and 37708. After we will calculate the factors of 37697 and 37708 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 37708

Prime factors of 37708 are 2, 11, 857. Prime factorization of 37708 in exponential form is:

37708 = 2² × 11¹ × 857¹

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 37708

List of positive integer factors of 37708 that divides 37697 without a remainder.

1, 2, 4, 11, 22, 44, 857, 1714, 3428, 9427, 18854

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37697 and 37708. The biggest common factor number is the GCF number.
So the greatest common factor 37697 and 37708 is 11.

Also check out the Least Common Multiple of 37697 and 37708