What is the Greatest Common Factor of 36270 and 36288?

Greatest common factor (GCF) of 36270 and 36288 is 18.

GCF(36270,36288) = 18

We will now calculate the prime factors of 36270 and 36288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36270 and 36288.

How to find the GCF of 36270 and 36288?

We will first find the prime factorization of 36270 and 36288. After we will calculate the factors of 36270 and 36288 and find the biggest common factor number .

Step-1: Prime Factorization of 36270

Prime factors of 36270 are 2, 3, 5, 13, 31. Prime factorization of 36270 in exponential form is:

36270 = 2¹ × 3² × 5¹ × 13¹ × 31¹

Step-2: Prime Factorization of 36288

Prime factors of 36288 are 2, 3, 7. Prime factorization of 36288 in exponential form is:

36288 = 2⁶ × 3⁴ × 7¹

Step-3: Factors of 36270

List of positive integer factors of 36270 that divides 36270 without a remainder.

1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 30, 31, 39, 45, 62, 65, 78, 90, 93, 117, 130, 155, 186, 195, 234, 279, 310, 390, 403, 465, 558, 585, 806, 930, 1170, 1209, 1395, 2015, 2418, 2790, 3627, 4030, 6045, 7254, 12090, 18135

Step-4: Factors of 36288

List of positive integer factors of 36288 that divides 36270 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 64, 72, 81, 84, 96, 108, 112, 126, 144, 162, 168, 189, 192, 216, 224, 252, 288, 324, 336, 378, 432, 448, 504, 567, 576, 648, 672, 756, 864, 1008, 1134, 1296, 1344, 1512, 1728, 2016, 2268, 2592, 3024, 4032, 4536, 5184, 6048, 9072, 12096, 18144

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36270 and 36288. The biggest common factor number is the GCF number.
So the greatest common factor 36270 and 36288 is 18.

Also check out the Least Common Multiple of 36270 and 36288