What is the Greatest Common Factor of 27538 and 27552?

Greatest common factor (GCF) of 27538 and 27552 is 14.

GCF(27538,27552) = 14

We will now calculate the prime factors of 27538 and 27552, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27538 and 27552.

How to find the GCF of 27538 and 27552?

We will first find the prime factorization of 27538 and 27552. After we will calculate the factors of 27538 and 27552 and find the biggest common factor number .

Step-1: Prime Factorization of 27538

Prime factors of 27538 are 2, 7, 281. Prime factorization of 27538 in exponential form is:

27538 = 2¹ × 7² × 281¹

Step-2: Prime Factorization of 27552

Prime factors of 27552 are 2, 3, 7, 41. Prime factorization of 27552 in exponential form is:

27552 = 2⁵ × 3¹ × 7¹ × 41¹

Step-3: Factors of 27538

List of positive integer factors of 27538 that divides 27538 without a remainder.

1, 2, 7, 14, 49, 98, 281, 562, 1967, 3934, 13769

Step-4: Factors of 27552

List of positive integer factors of 27552 that divides 27538 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 41, 42, 48, 56, 82, 84, 96, 112, 123, 164, 168, 224, 246, 287, 328, 336, 492, 574, 656, 672, 861, 984, 1148, 1312, 1722, 1968, 2296, 3444, 3936, 4592, 6888, 9184, 13776

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27538 and 27552. The biggest common factor number is the GCF number.
So the greatest common factor 27538 and 27552 is 14.

Also check out the Least Common Multiple of 27538 and 27552