What is the Greatest Common Factor of 27200 and 27216?

Greatest common factor (GCF) of 27200 and 27216 is 16.

GCF(27200,27216) = 16

We will now calculate the prime factors of 27200 and 27216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27200 and 27216.

How to find the GCF of 27200 and 27216?

We will first find the prime factorization of 27200 and 27216. After we will calculate the factors of 27200 and 27216 and find the biggest common factor number .

Step-1: Prime Factorization of 27200

Prime factors of 27200 are 2, 5, 17. Prime factorization of 27200 in exponential form is:

27200 = 2⁶ × 5² × 17¹

Step-2: Prime Factorization of 27216

Prime factors of 27216 are 2, 3, 7. Prime factorization of 27216 in exponential form is:

27216 = 2⁴ × 3⁵ × 7¹

Step-3: Factors of 27200

List of positive integer factors of 27200 that divides 27200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 64, 68, 80, 85, 100, 136, 160, 170, 200, 272, 320, 340, 400, 425, 544, 680, 800, 850, 1088, 1360, 1600, 1700, 2720, 3400, 5440, 6800, 13600

Step-4: Factors of 27216

List of positive integer factors of 27216 that divides 27200 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 54, 56, 63, 72, 81, 84, 108, 112, 126, 144, 162, 168, 189, 216, 243, 252, 324, 336, 378, 432, 486, 504, 567, 648, 756, 972, 1008, 1134, 1296, 1512, 1701, 1944, 2268, 3024, 3402, 3888, 4536, 6804, 9072, 13608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27200 and 27216. The biggest common factor number is the GCF number.
So the greatest common factor 27200 and 27216 is 16.

Also check out the Least Common Multiple of 27200 and 27216