What is the Greatest Common Factor of 36704 and 36708?

Greatest common factor (GCF) of 36704 and 36708 is 4.

GCF(36704,36708) = 4

We will now calculate the prime factors of 36704 and 36708, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36704 and 36708.

How to find the GCF of 36704 and 36708?

We will first find the prime factorization of 36704 and 36708. After we will calculate the factors of 36704 and 36708 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 36708

Prime factors of 36708 are 2, 3, 7, 19, 23. Prime factorization of 36708 in exponential form is:

36708 = 2² × 3¹ × 7¹ × 19¹ × 23¹

Step-3: Factors of 36704

List of positive integer factors of 36704 that divides 36704 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

Step-4: Factors of 36708

List of positive integer factors of 36708 that divides 36704 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 19, 21, 23, 28, 38, 42, 46, 57, 69, 76, 84, 92, 114, 133, 138, 161, 228, 266, 276, 322, 399, 437, 483, 532, 644, 798, 874, 966, 1311, 1596, 1748, 1932, 2622, 3059, 5244, 6118, 9177, 12236, 18354

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36704 and 36708. The biggest common factor number is the GCF number.
So the greatest common factor 36704 and 36708 is 4.

Also check out the Least Common Multiple of 36704 and 36708