What is the Greatest Common Factor of 27577 and 27584?

Greatest common factor (GCF) of 27577 and 27584 is 1.

GCF(27577,27584) = 1

We will now calculate the prime factors of 27577 and 27584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27577 and 27584.

How to find the GCF of 27577 and 27584?

We will first find the prime factorization of 27577 and 27584. After we will calculate the factors of 27577 and 27584 and find the biggest common factor number .

Step-1: Prime Factorization of 27577

Prime factors of 27577 are 11, 23, 109. Prime factorization of 27577 in exponential form is:

27577 = 11¹ × 23¹ × 109¹

Step-2: Prime Factorization of 27584

Prime factors of 27584 are 2, 431. Prime factorization of 27584 in exponential form is:

27584 = 2⁶ × 431¹

Step-3: Factors of 27577

List of positive integer factors of 27577 that divides 27577 without a remainder.

1, 11, 23, 109, 253, 1199, 2507

Step-4: Factors of 27584

List of positive integer factors of 27584 that divides 27577 without a remainder.

1, 2, 4, 8, 16, 32, 64, 431, 862, 1724, 3448, 6896, 13792

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27577 and 27584. The biggest common factor number is the GCF number.
So the greatest common factor 27577 and 27584 is 1.

Also check out the Least Common Multiple of 27577 and 27584