What is the Greatest Common Factor of 36686 and 36704?

Greatest common factor (GCF) of 36686 and 36704 is 2.

GCF(36686,36704) = 2

We will now calculate the prime factors of 36686 and 36704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36686 and 36704.

How to find the GCF of 36686 and 36704?

We will first find the prime factorization of 36686 and 36704. After we will calculate the factors of 36686 and 36704 and find the biggest common factor number .

Step-1: Prime Factorization of 36686

Prime factors of 36686 are 2, 13, 17, 83. Prime factorization of 36686 in exponential form is:

36686 = 2¹ × 13¹ × 17¹ × 83¹

Step-2: Prime Factorization of 36704

Prime factors of 36704 are 2, 31, 37. Prime factorization of 36704 in exponential form is:

36704 = 2⁵ × 31¹ × 37¹

Step-3: Factors of 36686

List of positive integer factors of 36686 that divides 36686 without a remainder.

1, 2, 13, 17, 26, 34, 83, 166, 221, 442, 1079, 1411, 2158, 2822, 18343

Step-4: Factors of 36704

List of positive integer factors of 36704 that divides 36686 without a remainder.

1, 2, 4, 8, 16, 31, 32, 37, 62, 74, 124, 148, 248, 296, 496, 592, 992, 1147, 1184, 2294, 4588, 9176, 18352

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36686 and 36704. The biggest common factor number is the GCF number.
So the greatest common factor 36686 and 36704 is 2.

Also check out the Least Common Multiple of 36686 and 36704