What is the Greatest Common Factor of 36600 and 36608?

Greatest common factor (GCF) of 36600 and 36608 is 8.

GCF(36600,36608) = 8

We will now calculate the prime factors of 36600 and 36608, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36600 and 36608.

How to find the GCF of 36600 and 36608?

We will first find the prime factorization of 36600 and 36608. After we will calculate the factors of 36600 and 36608 and find the biggest common factor number .

Step-1: Prime Factorization of 36600

Prime factors of 36600 are 2, 3, 5, 61. Prime factorization of 36600 in exponential form is:

36600 = 2³ × 3¹ × 5² × 61¹

Step-2: Prime Factorization of 36608

Prime factors of 36608 are 2, 11, 13. Prime factorization of 36608 in exponential form is:

36608 = 2⁸ × 11¹ × 13¹

Step-3: Factors of 36600

List of positive integer factors of 36600 that divides 36600 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 61, 75, 100, 120, 122, 150, 183, 200, 244, 300, 305, 366, 488, 600, 610, 732, 915, 1220, 1464, 1525, 1830, 2440, 3050, 3660, 4575, 6100, 7320, 9150, 12200, 18300

Step-4: Factors of 36608

List of positive integer factors of 36608 that divides 36600 without a remainder.

1, 2, 4, 8, 11, 13, 16, 22, 26, 32, 44, 52, 64, 88, 104, 128, 143, 176, 208, 256, 286, 352, 416, 572, 704, 832, 1144, 1408, 1664, 2288, 2816, 3328, 4576, 9152, 18304

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36600 and 36608. The biggest common factor number is the GCF number.
So the greatest common factor 36600 and 36608 is 8.

Also check out the Least Common Multiple of 36600 and 36608