What is the Greatest Common Factor of 27264 and 27280?

Greatest common factor (GCF) of 27264 and 27280 is 16.

GCF(27264,27280) = 16

We will now calculate the prime factors of 27264 and 27280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27264 and 27280.

How to find the GCF of 27264 and 27280?

We will first find the prime factorization of 27264 and 27280. After we will calculate the factors of 27264 and 27280 and find the biggest common factor number .

Step-1: Prime Factorization of 27264

Prime factors of 27264 are 2, 3, 71. Prime factorization of 27264 in exponential form is:

27264 = 2⁷ × 3¹ × 71¹

Step-2: Prime Factorization of 27280

Prime factors of 27280 are 2, 5, 11, 31. Prime factorization of 27280 in exponential form is:

27280 = 2⁴ × 5¹ × 11¹ × 31¹

Step-3: Factors of 27264

List of positive integer factors of 27264 that divides 27264 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 71, 96, 128, 142, 192, 213, 284, 384, 426, 568, 852, 1136, 1704, 2272, 3408, 4544, 6816, 9088, 13632

Step-4: Factors of 27280

List of positive integer factors of 27280 that divides 27264 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 31, 40, 44, 55, 62, 80, 88, 110, 124, 155, 176, 220, 248, 310, 341, 440, 496, 620, 682, 880, 1240, 1364, 1705, 2480, 2728, 3410, 5456, 6820, 13640

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27264 and 27280. The biggest common factor number is the GCF number.
So the greatest common factor 27264 and 27280 is 16.

Also check out the Least Common Multiple of 27264 and 27280