What is the Greatest Common Factor of 27584 and 27590?

Greatest common factor (GCF) of 27584 and 27590 is 2.

GCF(27584,27590) = 2

We will now calculate the prime factors of 27584 and 27590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27584 and 27590.

How to find the GCF of 27584 and 27590?

We will first find the prime factorization of 27584 and 27590. After we will calculate the factors of 27584 and 27590 and find the biggest common factor number .

Step-1: Prime Factorization of 27584

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

27584 = 2⁶ × 431¹

Step-2: Prime Factorization of 27590

Prime factors of 27590 are 2, 5, 31, 89. Prime factorization of 27590 in exponential form is:

27590 = 2¹ × 5¹ × 31¹ × 89¹

Step-3: Factors of 27584

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

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

Step-4: Factors of 27590

List of positive integer factors of 27590 that divides 27584 without a remainder.

1, 2, 5, 10, 31, 62, 89, 155, 178, 310, 445, 890, 2759, 5518, 13795

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27584 and 27590. The biggest common factor number is the GCF number.
So the greatest common factor 27584 and 27590 is 2.

Also check out the Least Common Multiple of 27584 and 27590